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King's Maths School

Challenge 381: Seek the Sum

Can you find the sum of these two numbers without finding the numbers themselves?

Two numbers represented by a  and  b satisfy the conditions

a3+b3=75a^3+b^3 = 75

and

aba2+b2=13\frac{ab}{a^2+b^2} = \frac{1}{3}

Find the exact value of a + b.