Question

If x + y = 2 and $\frac{1}{x}+\frac{1}{y}=2$ then the value of $x^3+y^3$ is

• A. 1
• B. 4
• C. 3
• D. 2

Answer 1

The correct option is D 2

Given $x+y=2$ and $\frac{1}{x}+\frac{1}{y}=2$

$x+y=2$ .....($1$) and $x+y=2xy$....... ($2$)

on comparing both the equation ,we will get $xy=1$ ,......equ($3$)

Now from equ($1$), $(x+y{)}^3=2^3$

$x^3+y^3+3xy(x+y)=8$

$x^3+y^3+3\left(1\right)\left(2\right)=8$....... [use equ($1$) and equ($2$)]

$x^3+y^3=2$