Question

The sum of two numbers is 9 and their product is 20. Find the sum of their cubes

• A. $189$
• B. $130$
• C. $76$
• D. $39$

Answer 1

The correct option is A $189$

Let two number be $x$ and $y$
Given,$x+y=9$ and $xy=20$
Now,$x+y=9$
Squaring both the sides,
$(x+y{)}^2=9^2$
$=>x^2+y^2+2xy=81$
$=>x^2+y^2+2\left(20\right)=81$
$=>x^2+y^2+40=81$
$=>x^2+y^2=81-40$
$=>x^2+y^2=41$
Now,
$x^3+y^3=(x+y)(x^2-(x\left)\right(y)+y^2)$
$=\left(9\right)(41-20)$
$=9\left(21\right)$
$=189$