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Algebra

Blazing goIITian

 Joined: 25 Jul 2011 Post: 322
29 Mar 2012 12:08:37 IST
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8
469
Try this !!
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

HOW MANY positive INTEGER X which X AND X+99 are COMPLETE SQUARE?

Hot goIITian

Joined: 3 Feb 2012
Posts: 159
30 Mar 2012 10:02:46 IST
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I guess 1..

Hot goIITian

Joined: 14 Feb 2012
Posts: 191
30 Mar 2012 10:05:12 IST
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1...

Blazing goIITian

Joined: 27 Dec 2010
Posts: 1508
30 Mar 2012 11:09:18 IST
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x = m^2.

x + 99 = m^2 + 99 = z^2.

z^2 - m^2 = 9*11.

(z-m)(z+m) = 3*3*11.

(z,m) = (1,10), (49,50), (15,18) and its permutations.

done.

Scorching goIITian

Joined: 10 Feb 2012
Posts: 262
30 Mar 2012 11:11:03 IST
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i can give you the solutions.......2401..............................1....................it is't a guess man i had mathematical solution following

Scorching goIITian

Joined: 10 Feb 2012
Posts: 262
30 Mar 2012 11:11:56 IST
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.......18... to i missed it

Scorching goIITian

Joined: 10 Feb 2012
Posts: 262
30 Mar 2012 11:13:22 IST
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sorry 15^2=225 is also a solution and not 18

Blazing goIITian

Joined: 25 Jul 2011
Posts: 322
30 Mar 2012 12:38:24 IST
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Hemang is absolutely Right...Nice work Bhaiya :)

Blazing goIITian

Joined: 25 Jul 2011
Posts: 322
30 Mar 2012 12:40:02 IST
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Hemang is absolutely Right...Nice work Bhaiya :)

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