Question

If the sum of two numbers is $11$ and sum of their cubes is $737$, find the sum of their squares.

Answer 1

Given

$a+b=11$

$a^3+b^3=737$

$(a+b{)}^3=a^3+b^3+3ab(a+b)$

$(11{)}^3=737+3ab(11)$

$1331=737+3ab\left(11\right)$

$3ab=\frac{1331-732}{11}$

$3ab=54$

$ab=18$

$(a+b{)}^2=a^2+b^2+2ab$

$121=a^2+b^2+36$

$a^2+b^2=85$.