If a+b+c=4, a b+b c+c a=-14 and a b c=18, then the value of \sqrt{4 a^{3}+4 b^{3}+4 c^{3}-36} will be

SSC CHSL 19 Apr 2021 Shift 3 Paper

Section: Quantitative Aptitude

Question : 58 of 100

Marks: +1, -0

a+b+c=4, a b+b c+c a=-14

and

a b c=18

, then the value of

√{4 a^{3}+4 b^{3}+4 c^{3}-36}

will be

Solution:

Given,

a+b+c=4

a b+b c+c a=-14

and

a b c=-18

∴ (a+b+c)^{2}=a^{2}+b^{2}+c^{2}

+2(a b+b c+c a)

⇒ a^{2}+b^{2}+c^{2}=(4)^{2}-2 ×(-14)=44

∴

The value of

√{4 a^{3}+4 b^{3}+4 c^{3}-36}

=√{4(a^{3}+b^{3}+c^{3})-36}

=√{4[(a+b+c)(a^{2}+b^{2}+c^{2}-a b

-b c-c a)+3 a b c]-36

=√{4 ×[4 ×(44+14)+3 ×-18]-36}

=√{676}=26

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