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If alpha, beta ar the roots of the quadr...

If `alpha, beta` ar the roots of the quadratic equation `x ^(2) -(3+ 2 ^(sqrt(log _(2)3))-3 ^(sqrt(log _(3)2)))x-2 (3 ^(log _(3)2)-2^(log _(z)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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