4x-2-2x-1-x-2-x-gt-1-

Question Number 198228 by sulaymonnorboyev140 last updated on 14/Oct/23

{(4 x^{2} + 2 x + 1)}^{x^{2} - x} > 1

Answered by MM42 last updated on 14/Oct/23

{\begin{cases} 4 x^{2} + 2 x + 1 > 1 \\ x^{2} - x > 0 \end{cases} \Rightarrow (- \infty, - \frac{1}{2}) \cup (0, + \infty) = A & (- \infty, 0) \cup (1, + \infty) = B

\Rightarrow A \cap B = (- \infty, - \frac{1}{2}) \cup (1, + \infty) (i)

{\begin{cases} 0 < 4 x^{2} + 2 x + 1 < 1 \\ x^{2} - x < 0 \end{cases} \Rightarrow (- \frac{1}{2}, 0) = C & (0, 1) = D

\Rightarrow C \cap D = ϕ (i i)

(i) \cup (i i) = (i)

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