Question

If $x+y=5$ and $x^2+y^2=111$. then value of $x^3+y^3$ is

• A. $770$
• B. $227$
• C. $555$
• D. $115$

Answer 1

The correct option is A $770$

Given: $x+y=5$ and $x^2+y^2=111$

Since, $(x+y{)}^2=x^2+y^2+2xy$ ........(1)

By putting the value of $x+y$ and $x^2+y^2$ in (1). we get
$5^2=111+2xy$

$\Rightarrow 25=111+2xy$

$\Rightarrow -86=2xy$

$\Rightarrow xy=-43$

Since, $(x+y{)}^3=x^3+y^3+3xy(x+y)$ .........(2)

By putting the value of $x+y$ and $xy$ in (2). we get

$5^3=x^3+y^3+3(-43)\left(5\right)$

$\Rightarrow 125=x^3+y^3-645$

$\Rightarrow x^3+y^3=770$

Option A is correct.