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Algebra
boywholived
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19 Mar 2012 15:35:23 IST
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little tough
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Algebra

Find the maximum value of x for which the equation            

 

x2-19x+94

          

is a perfect square


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boywholived
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19 Mar 2012 15:35:53 IST
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i mean x^2-19x+94
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boywholived
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19 Mar 2012 15:38:10 IST
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like it if you find it tough
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Neha
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19 Mar 2012 17:09:06 IST
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x=13 (provided x has to be an interger)
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WIll b iitan
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19 Mar 2012 18:45:42 IST
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13
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boywholived
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20 Mar 2012 15:54:59 IST
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right answer pls post the step
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hemang
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21 Mar 2012 12:29:42 IST
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x^2 - 19x + 94 = (x - 19/2)^2 + 15/4 = m^2

(2x - 19)^2 + 15 = 4m^2.

-15 = (2x - 19 - 2m)(2x - 19 + 2m)

15 = (19 + 2m - 2x)(2x - 19 + 2m).

15 = 15*1 = 3*5 = -3*-5 = -15*-1.

no we can equate this.

19 + 2m - 2x = 1. and 2x - 19 + 2m = 15.

x - m = 9. and x + m = 17.

so, at x = 13, m = 4.

similarly all solutions are =

m = + 4, - 4 , x = 13

m = +4, -4, x = 6.

m = +2, -2, x = 10.

m = +2, -2, x = 9.

the answer is 13...

:)
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