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Question

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


A
770
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B
227
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C
555
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D
115
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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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