Question

If a+b+c=10 and a²+b²=58,find the value of a³+b³

Answer 1

Given:$a+b=10$
$a^2+b^2=58$
Since, $(a+b{)}^2=a^2+b^2+2ab$
${10}^2=58+2ab$
100 = 58 + 2ab
42 = 2ab
ab = 21

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

${10}^3=a^3+b^3+3ab(a+b)$

$1000=a^3+b^3+3\times 21\left(10\right)$

$1000=a^3+b^3+630$

$\therefore a^3+b^3=370$