If a^{2}+b^{2}+c^{2}+170=2(8 a+5 b-9 c) then the value of \sqrt{4 a+8 b-c} will be

SSC CHSL 13 Apr 2021 Shift 3 Paper

Section: Quantitative Aptitude

Question : 71 of 100

Marks: +1, -0

a^{2}+b^{2}+c^{2}+170=2(8 a+5 b-9 c)

then the value of

√{4 a+8 b-c}

will be

Solution:

Given,

a^{2}+b^{2}+c^{2}+170

=2(8 a+5 b-9 c)

⇒ a^{2}+b^{2}+c^{2}+170

=16 a+10 b-18 c

⇒ a^{2}-16 a+64+b^{2}-10 b+25+c^{2}

+18 c+81=0

⇒ \;\; (a-8)^{2}+(b-5)^{2}+(c+9)^{2}=0

∴ \;\; a-8=0 ⇒ a=8

b-5=0 ⇒ b=5

and

c+9=0 ⇒ x=-9

∴ \;√{4 a+8 b-c}=√{4 × 8+8 × 5+9}

\;\; =√{32+40+9}=√{81}=9

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