SSC CGL 12 Aug 2017 Shift 1 Paper

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Question : 61 of 100

Marks: +1, -0

If

x(2 x+3)=90

and

7 y^{-1 / 2}+2 y^{-1 / 2}=y^{1 / 2}(x { \and } y

are positive numbers), then what is the value of

x^{2}+y^{2} ?

45
109
117
126

Solution:

x(2 x+3)=90

⇒

2 x^{2}+3 x-90=0

⇒

2 x^{2}+15 x-12 x-90=0

⇒

x(2 x+15)-6(2 x+15)=0

⇒

(2 x+15)(x-6)=0

\∴ x=6,- {15}/{2}

∵

7 y^{-1 / 2}+2 y^{-1 / 2}=y^{1 / 2}

⇒

{49}/{y}+ {4}/{y}+ {28}/{y}=y

⇒

81=y^{2}

⇒

y=√{81}

∴

y=9

So,

x^{2}+y^{2} =(6)^{2}+(9)^{2}

=36+81=117

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