Question

if x-y=4 and xy=12 find value of x^3-y^3

Answer 1

Given :-

$\sf\bullet{ x-y\:=\:4 }$

$\sf\bullet{ xy\:=\:12 }$

To find :-

$\sf\bullet{ \ x^{3}- \ y^{3}}$

Formula used !

$\bigstar{\boxed{\sf{ \ x^{3}- \ y^{3}\:=\:(x-y)( \ x^{2}+ \ y^{2}+xy )}}}$

Solution :-

x²+y² can be written as (x-y)²+2xy

So,

${\sf{ \ x^{3}- \ y^{3}\:=\:(x-y)[\ (x-y)^{2}+2xy+xy]}}$

${\sf{ \ x^{3}- \ y^{3}\:=\:(x-y)[\ (x-y)^{2}+3xy]}}$

$\tt{Now\:put\:the\:value}$

→$\sf{4×(16+36)}$

→$\sf{4×52}$

→$\sf{208}$

${ \mathbb{ \boxed{ \ x^{3}- \ y^{3}\:=\: 208}}}$