Algebra

Scorching goIITian

Joined: 10 Feb 2012
Post: 262
19 Mar 2012 15:35:23 IST
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little tough
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

Find the maximum value of x for which the equation            

 

x2-19x+94

          

is a perfect square



Comments (6)


Scorching goIITian

Joined: 10 Feb 2012
Posts: 262
19 Mar 2012 15:35:53 IST
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i mean x^2-19x+94

Scorching goIITian

Joined: 10 Feb 2012
Posts: 262
19 Mar 2012 15:38:10 IST
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like it if you find it tough

New kid on the Block

Joined: 19 Mar 2012
Posts: 11
19 Mar 2012 17:09:06 IST
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x=13 (provided x has to be an interger)


Cool goIITian

Joined: 19 Mar 2012
Posts: 46
19 Mar 2012 18:45:42 IST
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13

Scorching goIITian

Joined: 10 Feb 2012
Posts: 262
20 Mar 2012 15:54:59 IST
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right answer pls post the step
hemang's Avatar

Blazing goIITian

Joined: 27 Dec 2010
Posts: 1508
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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