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If (7+4sqrt(3))^(x^(2-8))+(7-4sqrt(3))^(...

If `(7+4sqrt(3))^(x^(2-8))+(7-4sqrt(3))^(x^(2-8))=14, then x=`

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The correct Answer is:
6
Sum of solutions ………..
Take `(7+4sqrt(3))^(x^(2)-4x+3)=t`
`(7+4sqrt(3))^(x^(2)-4x+3)=t` thus, equastion becomes
`t+(1)/(t)=14, t^(2)-14t+1=0`
`t = (14+-8sqrt(3))/(2) = 7 +-4sqrt(3)`
thus `x^(2)-4x+3=1, -1 implies x = 2,2 +- sqrt(2)`
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