Question

Помогите решить уравнение! $\sqrt{x+17} - \sqrt{x-7} = 4$

Answer 1

$\sqrt{x+17}-\sqrt{x-7}=4\; ,\; \; ODZ:\; \left \{ {{x+17 \geq 0} \atop {x-7 \geq 0}} \right. \; \left \{ {{x \geq -17} \atop {x \geq 7}} \right. \; ,\; x \geq 7\\\\\sqrt{x+17}= \sqrt{x-7}+4\\\\x+17=x-7+8 \sqrt{x-7}+16\\\\8\sqrt{x-7}=8\\\\\sqrt{x-7}=1\\\\x-7=1\\\\x=8\ \textgreater \ 7\\\\Otvet:\; \; x=8\; .$