кто шарит!помогите решить уравнение. Created by tarantyll. algebra-ru

кто шарит!помогите решить уравнение...

tarantyll @tarantyll

June 2022 1 5 Report

кто шарит!помогите решить уравнение

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ndusha

Verified answer

$\frac{2}{X^2+10x+25}- \frac{10}{25-x^2}= \frac{1}{x-5} \\ \frac{2}{X^2+2*5x+5^2}- \frac{10}{5^2-x^2}= \frac{1}{x-5} \\ \frac{2}{(x+5)^2}+ \frac{10}{x^2-5^2}= \frac{1}{x-5} \\ \frac{2}{(x+5)^2}+ \frac{10}{(x-5)(x+5)}= \frac{1}{x-5} \\ \frac{2(x-5)}{(x+5)^2(x-5)}+ \frac{10(x+5)}{(x-5)(x+5)^2}= \frac{(x+5)^2}{(x-5)(x+5)^2} \\ \frac{2(x-5)+10(x+5)-(x+5)^2}{(x-5)(x+5)^2} =0 \\ ODZ x \neq 5 ; x \neq -5 \\ 2(x-5)+10(x+5)-(x+5)^2=0 \\2x-10+10x+50-x^2-10x-25=0 \\2x+15-x^2=0 \\ x^2-2x-15=0$
D = (-2)² - 4·1·(-15) = 4 + 60 = 64
x1 = (2 - √64)/(2*1) = (2 - 8)/2 = -6/2 = -3
x1 = (2 + √64)/(2*1) = (2 + 8)/2 = 10/2 = 5 -не подходит по ОДЗ

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