SSC CHSL 11 Aug 2021 Shift 2 Paper

Section: Quantitative Aptitude

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Question : 56 of 100

Marks: +1, -0

x, y

are two positive numbers such that

x > y

. If

x^{4}+y^{4}=706

and

x y=15

, then the value of

2 x+3 y

is

19
20
18
15

Solution:

Given,

x^{4}+y^{4}=706

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

[ ∵ (a+b)^{2}=a^{2}+b^{2}+2 a b]

⇒(x^{2}+y^{2})^{2}=706+2 ×(15)^{2}

[ ∵ x y=15

(given)

]

⇒(x^{2}+y^{2})^{2}=706+450=1156

x^{2}+y^{2}=√{1156}=34

Now,

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

=34+2 × 15=64

∴ \;\; x+y=8 \;\;

. . .(i)
nd

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

=34-2 × 15=4

∴ \;\; x-y=2

. . . (ii)
On solving Eqs. (i) and (ii);

x=5

and

y=3

∴ \;\; 2 x+3 y=2 × 5+3 × 3

=10+9=19

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