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Solve log(1//2)(x^(2)-6x+12) ge -2....

Solve `log_(1//2)(x^(2)-6x+12) ge -2`.

Text Solution

Verified by Experts

The correct Answer is:
` x in [2, 4]`
`x^(2) - 6x+ 12 le (1/2)^(-2)`
` or x^(2) - 6x + 8 le 0`
` or (x-2)(x-4) le 0`
` rArr x in [2, 4]`
`"Also, " x^(2) - 6x+12 gt 0 or (x-3)^(2) + 3 gt 0" which is true for any real x. Hence, "x in [2, 4]`.
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