Question

2/(x ^ 2 + 5x) + 2/(2x - 10) = 15/(x ^ 2 - 25)

Answer 1

Ответ:

$x_{1}=4+\sqrt{26}\\x_{2}=4-\sqrt{26}$

Объяснение:

$\frac{2}{x^2+5x} +\frac{2}{2x-10} =\frac{15}{x^2-25} \\\\\frac{2}{x(x+5)} +\frac{2}{2(x-5)} =\frac{15}{(x-5)(x+5)} \\\\\frac{4(x-5)}{2x(x+5)(x-5)} +\frac{2x(x+5)}{2x(x-5)(x+5)} =\frac{30x}{2x(x-5)(x+5)} \\\\4(x-5)+2x(x+5)=30x\\4x-20+2x^2+10x=30x\\2x^2-16x-20=0\\x^2-8x-10=0\\D=64-4*1*(-10)=64+40=104\\x_{1}=\frac{8+\sqrt{104} }{2} =\frac{8+2\sqrt{26} }{2}=4+\sqrt{26}\\x_{2}=\frac{8-\sqrt{104} }{2} \frac{8+2\sqrt{26} }{2}=4-\sqrt{26}$