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How many integer values of `x` satisfy the inequality `(32)/(243) lt ((2)/(3))^(x^(2)) lt (9)/(4) ((8)/(27))^(x)`A. `3`B. `4`C. `0`D. `2` |
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Answer» Correct Answer - A `((2)/(3))^(5) lt ((2)/(3))^(x^(2)) lt ((2)/(3))^(-2) lt ((2)/(3))^(3x)` `rArr x^(2) lt 5` and `x^(2) gt -2 + 3x` `sqrt5 lt x lt sqrt(5) cap x^(2) - 3x + 2 gt 0` `(x - 2) ( x- 1) gt 0` `x lt 1 cup x gt 2` so `(-sqrt(5) lt x lt 1) cup (2 lt x lt sqrt5)` |
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