Question

If x + y = 5; $x^2+y^2=13$ then the value of $x^3+y^3$ is:

• A. 34
• B. 36
• C. 35
• D. 37

Answer 1

Answer: (C)

35

Given $x+y=5$......equ($1$) and $x^2+y^2=13$.......equ($2$)

$(x+y{)}^2=x^2+y^2+2xy=25$

$13+2xy=25$ [using equ($2$)]

$xy=6$....equ($3$)

Now from equ($1$), $(x+y{)}^3=5^3$

$x^3+y^3+3xy(x+y)=125$

$x^3+y^3+3\left(6\right)\left(5\right)=125$....... [use equ($1$) and equ($2$)]

$x^3+y^3=125-90=35$