tag:blogger.com,1999:blog-2217022227008948602.post3825318712870043210..comments2019-03-21T19:56:19.431-07:00Comments on The Puzzle Page: Simple AlgebraUnknownnoreply@blogger.comBlogger22125tag:blogger.com,1999:blog-2217022227008948602.post-59294265577978849422009-10-21T10:09:46.724-07:002009-10-21T10:09:46.724-07:00These are all the solutions to these equations.These are all the solutions to these equations.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2217022227008948602.post-3752869838204502582009-10-21T10:07:56.458-07:002009-10-21T10:07:56.458-07:00After 20 comments still no correct answer! I liked...After 20 comments still no correct answer! I liked the people who thought 25 + 9 = 36 though. Anyway, here's my effort:<br /><br />Several people have correctly established that xy = 14 (1)<br /><br />From (x + y)^2 = 64 it is clear that x+y = 8 (2a) or x+y = -8 (2b)<br /><br />subbing equation 1 into equation 2 (or vice versa) yields the equation:<br />x^2 - 8x + 14 = 0<br /><br />solving this leads to the solutions x = 4 + sqrt(2) and <br />x = 4 - sqrt(2).<br />Subbing these values back in equation (2a) yields values for y.<br /><br />Going back and doing the same thing with equations (1) and (2b) eventually leads to the four solutions:<br />x = 4 + sqrt(2), y = 4 - sqrt(2)<br />x = 4 - sqrt(2), y = 4 + sqrt(2)<br />x = -4 + sqrt(2), y = -4 - sqrt(2)<br />x = -4 - sqrt(2), y = -4 + sqrt(2) <br /><br />The first 2 of these were stated as decimals further up the page.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2217022227008948602.post-48158979784223121172009-10-19T00:13:17.710-07:002009-10-19T00:13:17.710-07:00simple: 64=x*x+y*y+2xy
but x*x+y*y=36so
2xy=64-36
...simple: 64=x*x+y*y+2xy<br />but x*x+y*y=36so<br />2xy=64-36<br />xy=28/2<br />xy=14abishekhttps://www.blogger.com/profile/17038040238528638576noreply@blogger.comtag:blogger.com,1999:blog-2217022227008948602.post-74485424824937278912009-06-30T17:18:00.652-07:002009-06-30T17:18:00.652-07:00Somebody was on the right track earlier. One of t...Somebody was on the right track earlier. One of the equations is a circle with radius 6 centered at origin. The other equation yields two straight lines with slope -1. Both of these lines intersect the circle, so there are four solutions. The distance of these lines from the origin is 5.6569, or 4*sqrt(2), so these lines do indeed intersect the circle. The y intercept of one line is +8 and the y intercept of the second line is -8fishavenuehttps://www.blogger.com/profile/01536594763014769926noreply@blogger.comtag:blogger.com,1999:blog-2217022227008948602.post-15382309060576895992009-06-18T19:59:36.990-07:002009-06-18T19:59:36.990-07:00http://www05.wolframalpha.com/input/?i=solve+{x%C2...http://www05.wolframalpha.com/input/?i=solve+{x%C2%B2%2By%C2%B2+%3D+36%2C+(x%2By)%C2%B2+%3D+64}Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2217022227008948602.post-69780957572128035202009-03-14T23:53:00.000-07:002009-03-14T23:53:00.000-07:00@Louie:25+9 is NOT EQUAL to 36.25+9=34so your solu...@Louie:<BR/><BR/>25+9 is NOT EQUAL to 36.<BR/>25+9=34<BR/><BR/>so your solution is incorrect. :-)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2217022227008948602.post-21191371484403046792009-03-11T16:51:00.000-07:002009-03-11T16:51:00.000-07:00to put things simpiliar x^2 + y^2 = 36.x = 3y = 53...to put things simpiliar x^2 + y^2 = 36.<BR/><BR/>x = 3<BR/>y = 5<BR/>3^2 = 9<BR/>5^2 = 25<BR/>25+9=36<BR/><BR/><BR/><BR/>(x+y)^2 = 64<BR/>(3+5) ^2 = 64<BR/>(8) ^2 = 64<BR/>8x8=64<BR/><BR/>So 3x5 = 15 not what you others are saying as 14. It is not 7 and 2Louiehttps://www.blogger.com/profile/04335285026219523328noreply@blogger.comtag:blogger.com,1999:blog-2217022227008948602.post-57261595246712345522009-03-11T08:34:00.000-07:002009-03-11T08:34:00.000-07:00this is really easy. so x is 3 and y is 5. 3 to th...this is really easy. so x is 3 and y is 5. 3 to the 2nd power is 9 5 to the second power is 25 25+9=36. Then, x+y or 3+5 = 8 to the second power is 64 so x is 3 and y is 5Louiehttps://www.blogger.com/profile/04335285026219523328noreply@blogger.comtag:blogger.com,1999:blog-2217022227008948602.post-63375915990647080242009-03-05T02:31:00.000-08:002009-03-05T02:31:00.000-08:00You are all wrong. Start with (x+y)^2 = 64, so x+...You are all wrong. Start with (x+y)^2 = 64, so x+y = 8 <BR/><BR/>Then look at the equation (x^2+y^2)= 36.<BR/><BR/>We know that the two numbers x + y = 8 so if we look at 5 and 3 we get 25 + 9 = 36<BR/><BR/>so either x or y = 3 or 5<BR/><BR/>so the answer is not 14 its actually 15.<BR/><BR/>Hope you all agree its simple reallyAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-2217022227008948602.post-48116047451448391212008-12-04T20:47:00.000-08:002008-12-04T20:47:00.000-08:00(x+y)^2=64x+y=8(x+y)^2=64x^2+2xy+y^2=64x^2+y^2=362...(x+y)^2=64<BR/>x+y=8<BR/><BR/>(x+y)^2=64<BR/>x^2+2xy+y^2=64<BR/>x^2+y^2=36<BR/>2xy=28<BR/>xy=14<BR/><BR/>x+y=8<BR/>xy=14<BR/><BR/>x+y=8<BR/>0x+y=14/x<BR/><BR/>x=8-14/x<BR/>x^2-8x+14=0<BR/>quadratic equation<BR/><BR/>V is square root symbol<BR/><BR/>x=4+-V2 about 5.4<BR/>y= about 2.6Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2217022227008948602.post-35620789496948626582008-10-14T21:44:00.000-07:002008-10-14T21:44:00.000-07:00astronomical!!!ever!!astronomical!!!ever!!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2217022227008948602.post-68694225613928353682008-07-30T15:15:00.001-07:002008-07-30T15:15:00.001-07:001. x2+y2= 362.(x+y)2= (x+y)(x+y)= x2+y2+2xy=643. 3...1. x2+y2= 36<BR/>2.(x+y)2= (x+y)(x+y)= x2+y2+2xy=64<BR/>3. 36 + 2xy = 64<BR/>4. 2xy=28<BR/>5.xy = 14Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2217022227008948602.post-77627416779437955732008-07-30T15:15:00.000-07:002008-07-30T15:15:00.000-07:001. x2+y2= 362.(x+y)2= (x+y)(x+y)= x2+y2+2xy=643. 3...1. x2+y2= 36<BR/>2.(x+y)2= (x+y)(x+y)= x2+y2+2xy=64<BR/>3. 36 + 2xy = 64<BR/>4. 2xy=28<BR/>5.xy = 14Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2217022227008948602.post-77099139333059586312008-07-21T14:47:00.000-07:002008-07-21T14:47:00.000-07:00there is no answer. X2+Y2=36 is a circle from the ...there is no answer. X2+Y2=36 is a circle from the origin with the rediuce of 6. <BR/>(x+y)2=64 is two lines which pass A( 0,8 ), B ( 8,0) and C( 0,-8), D( -8 ,0 ). these lines and that circle have no intercetion.Naboshadwww.bsabah.blogfa.comnoreply@blogger.comtag:blogger.com,1999:blog-2217022227008948602.post-11772710282928411542008-07-11T17:24:00.000-07:002008-07-11T17:24:00.000-07:0064=(x+y)²=x²+y²+2xysince x²+y²=362xy=64-36=28(x-y)...64=(x+y)²=x²+y²+2xy<BR/>since x²+y²=36<BR/>2xy=64-36=28<BR/><BR/>(x-y)²=x²+y²-2xy=36-28=8<BR/><BR/>then x-y=2V2 or -2V2<BR/>(v=square root)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2217022227008948602.post-58965044487604825052008-04-02T22:10:00.000-07:002008-04-02T22:10:00.000-07:00The question "what is the value of x*y?" has been ...The question "what is the value of x*y?" has been answered already and it is 14.<BR/><BR/>If you had been wondering what is x and y, there are two possible set of answers.<BR/><BR/>#1.<BR/>x = 5.414213562<BR/>y = 2.585786438<BR/><BR/>#2. <BR/>x = 2.585786438<BR/>y = 5.414213562<BR/><BR/>x and y values were determined using the quadratic equation formula.elmerhttps://www.blogger.com/profile/17078171856087074045noreply@blogger.comtag:blogger.com,1999:blog-2217022227008948602.post-83475007072876778942008-03-28T16:10:00.000-07:002008-03-28T16:10:00.000-07:00It's obvious that xy=14, but that still does not a...It's obvious that xy=14, but that still does not answer the original question : what is y and what is x?Mhttps://www.blogger.com/profile/01803609024275592741noreply@blogger.comtag:blogger.com,1999:blog-2217022227008948602.post-54192986769134653242008-03-05T23:32:00.000-08:002008-03-05T23:32:00.000-08:00The problem is simple. Expand (x+y)squared and re...The problem is simple. Expand (x+y)squared and replace the value of Xsquared + Ysquared with 36.<BR/><BR/>we will arrive at 2xy = 64 -36<BR/><BR/>which gives xy =14Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2217022227008948602.post-42622930371390417572008-03-03T11:03:00.000-08:002008-03-03T11:03:00.000-08:00aargh, never mind, the product of the solutions is...aargh, never mind, the product of the solutions is c/b (c and b are the third and second degrees coefficients) so it is simply 14. I've done many unuseful calculations.Riccardo Antonelli (2)noreply@blogger.comtag:blogger.com,1999:blog-2217022227008948602.post-17366535881333129182008-02-29T09:08:00.000-08:002008-02-29T09:08:00.000-08:00The solution of the system gives four possible val...The solution of the system gives four possible values for x and y, and for all of them xy is 14.Riccardo Antonellinoreply@blogger.comtag:blogger.com,1999:blog-2217022227008948602.post-18416097042675689772008-02-03T20:34:00.000-08:002008-02-03T20:34:00.000-08:00It is possible, but the values of x and y are not ...It is possible, but the values of x and y are not integers.Erikhttps://www.blogger.com/profile/14514993727423832898noreply@blogger.comtag:blogger.com,1999:blog-2217022227008948602.post-31086637454485708402008-02-01T22:01:00.000-08:002008-02-01T22:01:00.000-08:00how can this be possible? i've gone through so man...how can this be possible? i've gone through so many combinations. i've gotten quite far, but at the last minute something turns out wrong. i don't want the answer, i just want to know whether or not it's actually possible.Anonymousnoreply@blogger.com