If a+b=1 and a b=-6, then what is the value of a^{3}+b^{3} ?

BA LLB Banaras Hindu University 2018 Solved Paper

Question : 120 of 170

Marks: +1, -0

a+b=1

and

a b=-6

, then what is the value of

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

Solution:

Given,

a+b=1

and

a b=-6

∴ (a+b)^{2}=a^{2}+b^{2}+2 a b

⇒ 1=a^{2}+b^{2}-12

⇒ \;\; a^{2}+b^{2}=13

∴ \;\; a^{3}+b^{3}=(a+b)(a^{2}+b^{2}-a b)

=1(13+6)=19

Alternate method (By Direct Method)
Let

a=3, b=-2

So,

\;\; a+b=3-2=1

a b=3 ×-2=-6

a^{3}+b^{3}=(3)^{3}+(-2)^{3}

=27-8=19

Go to Question:

Prev Question

Next Question