Question

A³+b³ if a+b=3ab=2
please help me​

Answer 1

`a^3 + b^3 = -4`

Explanation:

Given

`a + b = 3ab = 2`

Required

Solve:
`a^3 + b^3`

Rewrite the expression as:

`a^3 + b^3 = a^3 - a^2b +ab^2 + a^2b - ab^2 + b^3`

Factorize

`a^3 + b^3 = a(a^2 - ab +b^2) + b(a^2 - ab + b^2)`

`a^3 + b^3 = (a + b)(a^2 - ab + b^2)`

Rewrite as:

`a^3 + b^3 = (a + b)(a^2 + b^2- ab)`

`a^3 + b^3 = (a + b)(a^2 + b^2+2ab - 3ab)`

Factorize

`a^3 + b^3 = (a + b)((a + b)^2 - 3ab)`

Open brackets

`a^3 + b^3 = (a + b)^3 - 3ab(a + b)`

Given that:

`a + b = 3ab = 2`

This means that:

`a + b = 2` and
`3ab = 2`

So, we have:

`a^3 + b^3 = (a + b)^3 - 3ab(a + b)`

`a^3 + b^3 = 2^3 - 3 * 2 * 2`

`a^3 + b^3 = 8 - 12`

`a^3 + b^3 = -4`