Question

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

Answer 1

a³+ b³ = a³+3a²b+3ab²+b³

Answer 2

We have given that
a+b=10 and a^2+b^2=58

$a + b = 10 \\ on \: squaring \: both \: sides \\ {(a + b) }^{2} = 100$
a^2+b^2+2ab=100
58+2ab=100 (a^2+b^2=58)
2ab=100-58
2ab=42
ab=21


now according to the question,
a^3+b^3=(a+b)(a^2+b^2+2ab)
= (10)(58-21)
=(10)(37)
=370