Question 23

If the sum of two numbers is 13 and the sum of their squares is 97, what is their product?

Solution

$$(A+ B )^2 = A^2 + B^2 + 2\times A\times B$$

this is a algebraic identity we will use this in solving question

given

A + B = 13

$$A^2 + B^2$$ = 97

so

$$(A+ B )^2 = A^2 + B^2 + 2\times A\times B$$

$$(13)^2 = 97 + 2\times A\times B$$

169 = $$97 + 2\times A\times B$$

36 =$$A\times B$$

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