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

Solution

## 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$$5^3=x^3+y^3+3(-43)(5)$$$$\Rightarrow 125=x^3+y^3-645$$$$\Rightarrow x^3+y^3=770$$Option A is correct.Mathematics

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