Question

if (a+b)=10,a^2+b^2=56 then find the value of a^3+b^3 pls help

Answer 1

Answer:

hope this is correct and helps you..

Answer 2

Solution:

First we need to find the value of ab.

As,

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

Given that:

$a + b = 10 \: \: and \: \: a {}^{2} + b {}^{2} = 56 \\ \\ Now,\\ a {}^{2} + b {}^{2} = (a + b) {}^{2} - 2ab \\ \\ \implies \: 56 = 10 {}^{2} - 2ab \\ \\ \implies \: 2ab = 100 - 56 = 44 \\ \\ \implies \: ab = 22$

Now,

Using:

$a + b = 10 \: \: and \: \: ab = 44$

$a {}^{3} + b {}^{ 3} = (a + b) {}^{3} - 3ab(a + b) = 10 {}^{3} - 3(22)(10) = 1000 - 660 = 340$