Question

решите систему неравенств

Answer 1

Решение на фотографии

Answer 2

Ответ:

$\bigg [\dfrac{1}{7} \ ; \ 2 \bigg ]$

Объяснение:

$\displaystyle \left \{ {{2x-\dfrac{x+1}{2} \geq \dfrac{x-1}{3}} \atop {(x+5)(x-5)+37 \leq (x-6)^{2}}} \right. \Leftrightarrow \left \{ {{12x-3(x+1) \geq 2(x-1)} \atop {x^{2}-5^{2}+37 \leq x^{2}-2 \cdot x\cdot 6+6^{2}}} \right. \Leftrightarrow$

$\displaystyle \Leftrightarrow \left \{ {{12x-3x-3 \geq 2x-2} \atop {x^{2}-25+37 \leq x^{2}-12x+36}} \right. \Leftrightarrow \left \{ {{9x-2x \geq 3-2} \atop {x^{2}-x^{2}+12x \leq -12+36}} \right. \Leftrightarrow$

$\displaystyle \Leftrightarrow \left \{ {{7x \geq 1} \atop {12x \leq 24}} \right. \Leftrightarrow \left \{ {{x \geq \dfrac{1}{7}} \atop {x \leq 2}} \right. \Leftrightarrow x \in \bigg [\dfrac{1}{7} \ ; \ 2 \bigg ];$