Решите неравенство
[tex]0,5^{ x^{2} -9x+17,5} \geq \frac{8}{ \sqrt{2} } [/tex]
[tex]0,5^{ x^{2} -9x+17,5} \geq \frac{8}{ \sqrt{2} } [/tex]
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(1/2)^(x²-9x+17,5) ≥8/√2 ;((2)^(-1) )^(x²-9x+17,5) ≥ 2³/2^(1/2) ;
(2)^(-x²+9x-17,5) ≥ 2^(3-1/2) ;
-x²+9x-17,5 ≥ 2,5 ;
x² -9x +20 ≤ 0;
(x-4)(x-5) ≤ 0 ;
методом интервалов:
+ - +
----------- [4 ] ----- [ 5]----------:
x∈[4;5].
ответ: x∈[4;5].