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If `alpha` and `beta` are positive the the least value of `(alpha^(-6) + beta^(-6) + 2alpha^(-3)beta^(-3))alpha^(6)beta^(6)`where `alpha` =2 and `beta` =3.

A

16

B

25

C

30

D

36

Text Solution

Verified by Experts

The correct Answer is:
B
(i) Simplify the expression and find `(alpha + beta)` and `alpha beta`.
(ii) First find the sum of the roots and product of the roots.
(iii) `alpha^(-6) + beta^(-6) + (2)/(alpha^(3)beta^(3)) = ((alpha^(3) + beta^(3))/(alpha^(6)beta^(6)))`
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