Problem 1

Algebra Level 2

a^2 + b^2 = 7 and a^3 + b^3 = 10, then greatest value of a + b can be

9/2 4 6 5

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1 solution

Sanjay Balaji
Apr 7, 2014

a + b = x (say), then x^2 = a^2 + b^2 + 2ab. x^3 = a^3 + b^3 + 3ab (a + b) Eliminating ab, we get x^3 - 21x + 20 = 0 So, x = 1 or 4 or - 5.

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