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Algebra

Cool goIITian

Joined:	15 Jul 2007
Post:	75

1 Jan 2008 21:35:14 IST

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424

gbritish math olympiad

None

2. Find all solutions in positive integers x, y, z to the simultaneous

equations

x + y - z = 12

x^2 + y^2 -z^2 = 12.

british math olympiad

5. For positive real numbers a, b, c, prove that

(a^2+ b^2)^2

greater than or equal to (a + b + c)(a + b ? c)(b + c ? a)(c + a ? b).

6. Let n be an integer. Show that, if 2 + 2sqrt(1 + 12n^2)is an integer, then

it is a perfect square

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Comments (2)

Ambareesh Rishi

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Joined: 4 May 2007

Posts: 499

1 Jan 2008 21:43:46 IST

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what's " ? " in there or we have to guess what symbol is goin to be there and then solve it

Nadeem

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Joined: 25 Aug 2007

Posts: 521

1 Jan 2008 23:26:01 IST

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2. (x,y,z) are ( 18,23,29) , ( 14,45,47) , ( 15,34,37) . the values of x and y can be interchanged.

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