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Question

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


A
34
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B
36
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C
35
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D
37
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Solution

The correct option is A 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($$1$$),  $$(x+y)^3=5^3$$

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


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

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

Mathematics

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