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Solve (1/2)^(x^(6)-2x^(4)) lt 2^((x)^(2...

Solve ` (1/2)^(x^(6)-2x^(4)) lt 2^((x)^(2))`.

Text Solution

Verified by Experts

The correct Answer is:
` x in R - {0, pm 1}`
` (1/2)^(x^(6)-2x^(4))lt2^(x^(2))`
` or (1/2)^(x^(6)-2x^(4))lt(1/2)^(-x^(2))`
` or x^(6) - 2x^(4) gt -x^(2)`
` or x^(6) - 2x^(4) + x^(2) gt 0`
` or (x^(3)=x)^(2) gt 0`
` rArr x^(3) - x ne 0`
` :. x ne 0, - 1, 1`
` :. x in R - {0, pm 1}`
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