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If alpha, beta are the roots of the quad...

If `alpha, beta` are the roots of the quadratic equation `x^2 - 3x - 2(3^(log_3 2) - 2^(log_2 3))) = 0` then the value of `alpha^2 + alpha beta + beta^2` is equal to

A

`11`

B

`7`

C

`3`

D

`5`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `x^(2)-(3+2^(sqrt(log_(2)3))-3^(sqrt(log_(3)2)))x-2(3^(log_(3)2)-2^(log_(2)3))=0`
`implies x^(2)-3(x)-2(2-3)=0`
`implies x^(2)-3x+2=0`
`impliesalpha=2`, `beta=1`
`alpha^(2)+alphabeta+beta^(2)=4+2+1=7`
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