Question

даю 30б решите неравенство

Answer 1

$2^{(x-3)^{2}} \leq 4^{\frac{x^{2}-18}{2}}\\\\2^{(x-3)^{2}}\leq(2^{\frac{x^{2}-18}{2}})^{2}\\\\2^{(x-3)^{2}} \leq2^{x^{2}-18}\\\\2>1\Rightarrow (x-3)^{2}\leq x^{2}-18\\\\x^{2}-6x+9 \leq x^{2}-18 \\\\x^{2}-6x-x^{2}\leq-18-9\\\\-6x\leq-27\\\\x\geq4,5\\\\Otvet:\boxed{x\in[4,5;+\infty)}$

Answer 2

Решите неравенство   2^(x-3)² ≤ 4^( (x-18)/2)  

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2^(x-3)² ≤ (2²)^ ( (x²-18)/2 )  ⇔2^(x-3)² ≤ 2^ ( 2*(x²-18)/2 ) ⇔

2^(x-3)² ≤ 2^ ( x²-18 )    ||  2 >1 || ⇔  (x-3)²  ≤ x²- 18⇔x²-6x+9  ≤ x²- 18 ⇔

9+18 ≤  6x ⇔ 27 ≤ 6x  ⇔ x ≥ 4,5  ;  по другому   x ∈ [ 4,5 ;∞)

Ответ:  x ∈ [ 4,5 ;∞)