SSC CGL Tier II 1 Dec 2016 Paper 1

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Question : 74 of 100

Marks: +1, -0

If

a^{3}=117+b^{3}

and

a=3+b

then the value of

(a + b)

is :

± 7
± 49
± 13
0

Solution:

(1)

a^{3}-b^{3}=117 ; a-b=3

⇒(a-b) (a^{2}+b^{2}+a b )=117

⇒ 3 ×(a^{2}+b^{2}+a b )=117

⇒a^{2}+b^{2}+a b= {117}/{3}=39

⇒(a-b)^{2}+3 a b=39

⇒ 3^{2}+3 a b=39

⇒3 a b=39-9=30

⇒ a b= {30}/{3}=10

∴(a+b)^{2}=(a-b)^{2}+4 a b

=9+4 × 10=49

∴ a+b=√{49}=± 7

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