Question

a cube plus b cube upon a square + b square + ab = a + b prove that​

Answer 1

$\sf{To \ prove \ : \ {\dfrac{a^3 + b^3}{a^2 + b^2 + ab}} = a + b}$


$\sf{L.H.S. = {\dfrac{a^3 + b^3}{a^2 + b^2 + ab}}}$


${\boxed{\sf{a^3 + b^3 = (a + b)(a^2 + b^2 + ab)}}}$


$\sf{= {\dfrac{(a + b)(a^2 + b^2 + ab)}{a^2 + b^2 + ab}}}$


$\sf{= {\dfrac{(a + b)( {\cancel{a^2 + b^2 + ab}} )}{ {\cancel{a^2 + b^2 + ab}} }}}$


$\sf{= a + b}$


$\sf{= R.H.S.}$


$\sf{Hence, \ proved.}$