Допоможіть розв'язати 15.35 !!!
- + - +
______(- 1)_______[2]_______[3]________
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Ответ : x ∈ (- 1 ; 2] ∪ [3 , + ∞)
![(\sqrt{2}-1)^{\frac{6x-6}{x+1}}\leq(\sqrt{2}+1)^{-x}\\\\(\sqrt{2}-1)^{\frac{6x-6}{x+1}}\leq [(\sqrt{2}-1)^{-1}]^{-x}\\\\(\sqrt{2}-1)^{\frac{6x-6}{x+1}} \leq (\sqrt{2}-1)^{x}\\\\\frac{6x-6}{x+1}\leq x\\\\\frac{6x-6}{x+1}-x\leq0\\\\\frac{6x-6-x^{2}-x }{x+1}\leq0\\\\\frac{-x^{2}+5x-6 }{x+1}\leq0\\\\\frac{x^{2}-5x+6 }{x+1}\geq0\\\\\frac{(x-2)(x-3)}{x+1}\geq 0,x\neq-1](https://tex.z-dn.net/?f=%28%5Csqrt%7B2%7D-1%29%5E%7B%5Cfrac%7B6x-6%7D%7Bx%2B1%7D%7D%5Cleq%28%5Csqrt%7B2%7D%2B1%29%5E%7B-x%7D%5C%5C%5C%5C%28%5Csqrt%7B2%7D-1%29%5E%7B%5Cfrac%7B6x-6%7D%7Bx%2B1%7D%7D%5Cleq%20%5B%28%5Csqrt%7B2%7D-1%29%5E%7B-1%7D%5D%5E%7B-x%7D%5C%5C%5C%5C%28%5Csqrt%7B2%7D-1%29%5E%7B%5Cfrac%7B6x-6%7D%7Bx%2B1%7D%7D%20%5Cleq%20%28%5Csqrt%7B2%7D-1%29%5E%7Bx%7D%5C%5C%5C%5C%5Cfrac%7B6x-6%7D%7Bx%2B1%7D%5Cleq%20x%5C%5C%5C%5C%5Cfrac%7B6x-6%7D%7Bx%2B1%7D-x%5Cleq0%5C%5C%5C%5C%5Cfrac%7B6x-6-x%5E%7B2%7D-x%20%7D%7Bx%2B1%7D%5Cleq0%5C%5C%5C%5C%5Cfrac%7B-x%5E%7B2%7D%2B5x-6%20%7D%7Bx%2B1%7D%5Cleq0%5C%5C%5C%5C%5Cfrac%7Bx%5E%7B2%7D-5x%2B6%20%7D%7Bx%2B1%7D%5Cgeq0%5C%5C%5C%5C%5Cfrac%7B%28x-2%29%28x-3%29%7D%7Bx%2B1%7D%5Cgeq%200%2Cx%5Cneq-1 "(\sqrt{2}-1)^{\frac{6x-6}{x+1}}\leq(\sqrt{2}+1)^{-x}\\\\(\sqrt{2}-1)^{\frac{6x-6}{x+1}}\leq [(\sqrt{2}-1)^{-1}]^{-x}\\\\(\sqrt{2}-1)^{\frac{6x-6}{x+1}} \leq (\sqrt{2}-1)^{x}\\\\\frac{6x-6}{x+1}\leq x\\\\\frac{6x-6}{x+1}-x\leq0\\\\\frac{6x-6-x^{2}-x }{x+1}\leq0\\\\\frac{-x^{2}+5x-6 }{x+1}\leq0\\\\\frac{x^{2}-5x+6 }{x+1}\geq0\\\\\frac{(x-2)(x-3)}{x+1}\geq 0,x\neq-1")