Решить уравнение . (x^2-6x-9)/x=(x^2-4x-9)/(x^2-6x-9). Created by artemy050702. algebra-ru

(x^2-6x-9)...

July 2022 1 27 Report

Решить уравнение .
(x^2-6x-9)/x=(x^2-4x-9)/(x^2-6x-9)

Answers & Comments

tamarabernukho $\frac{x^2-6x-9}{x} = \frac{x^2-4x-9}{x^2-6x-9} \\ \\ (x^2-6x-9)^2=x(x^2-4x-9) \\ \\$

x=0 не является корнем уравнения, разделим обе части на x²

$\frac{x^2-6x-9}{x} * \frac{x^2-6x-9}{x}= \frac{x}{x} * \frac{x^2-4x-9}{x} \\ \\ (x-6- \frac{9}{x} )^2=x-4- \frac{9}{x} \\ \\ t=x- \frac{9}{x} \\ \\ (t-6)^2=t-4 \\ \\ t^2-12t+36=t-4 \\ \\ t^2-13t+40=0 \\ \\ D=9; t_{1} =(13+3)/2=8; t_{2} =(13-3)/2=5 \\ \\ 1)t=8;x- \frac{9}{x} =8;x^2-8x-9=0 \\ \\ D=64+36=100 \\ x_{1} =(8+10)/2=9 \\ x_{2} =(8-10)/2=-1 \\ \\ 2)t=5;x- \frac{9}{x} =5;x^2-5x-9=0 \\ \\ D=25+36=61\\ x_{3} =(5- \sqrt{61} )/2 \\ x_{4} =(5+ \sqrt{61} )/2\\ \\ \\$

4 votes Thanks 2

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