Question

If a^2 +b^2=ab find a^3+b^3

Answer 1

Step-by-step explanation:

$\bold{given \: by \:( {a}^{2} + {b}^{2} = ab}) \\ \bold{let} \: \bold{ {(a + b)}^{2} - 2ab \: = ( {a}^{2} + {b}^{2} )} \\ \: \bold{ {(a + b)}^{2} = 2ab + ab} \\ \bold{ {(a + b)}^{2} = 3ab} \\ (a + b) = \sqrt{3ab} \\ now \\ \bold{we \: find \: us \: \: {a}^{3} + {b}^{3} } \\ {a}^{3} + {b}^{3} = {(a + b)}^{3} + 3ab(a + b) \\ = { \sqrt{3ab} }^{3} + 3ab \times \sqrt{3ab} \\ = 2( { \sqrt{3ab} )}^{3}$