SSC CGL 17 Aug 2017 Shift 1 Paper

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Question : 62 of 100

Marks: +1, -0

If

a+b=4

and

a b=3

, then what is the value of

a^{3}+b^{3}\ ?

21
17
28
31

Solution:

a + b = 4

and

ab = 3

∵

(a+b)^{2}=a^{2}+b^{2}+2 a b

⇒

(4)^{2}=a^{2}+b^{2}+2 ∵ 3

⇒

16=a^{2}+b^{2}+6

⇒

a^{2}+b^{2}=16-6

⇒

a^{2}+b^{2}=10

∴

a^{3}+b^{3}=(a+b)

(a^{2}+b^{2}-a b )

=(4)(10-3)=4 × 7=28

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