SSC CHSL 13 Apr 2021 Shift 3 Paper

Section: Quantitative Aptitude

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Question : 59 of 100

Marks: +1, -0

If

x^{3}+y^{3}=468

and

x+y=12

then the value of

x^{4}+y^{4}

will be

3620
2036
3025
3026

Solution:

Given,

x^{3}+y^{3}=468

and

\;\; x+y=12

∵ x^{3}+y^{3}=(x+y)^{3}-3 x y(x+y)

⇒ \;\; 468=(12)^{3}-3 x y × 12

⇒ \;\; x y=\;{1728-468}/{36}=35

∴ (x+y)^{2}=x^{2}+y^{2}+2 x y

⇒(12)^{2}=x^{2}+y^{2}+2 × 35

[ ∵ x y=35]

⇒ \;\; x^{2}+y^{2}=144-70=74

Now,

(x^{2}+y^{2})^{2}=x^{4}+y^{4}+2 x^{2} y^{2}

∴ \;\; x^{4}+y^{4}=(74)^{2}-2 ×(35)^{2}

=5476-2450=3026

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