Срочно!!! Буду очень благодарна. Created by kristinakuts20. matematika-ru

Срочно!!! Буду очень благодарна...

kristinakuts20 @kristinakuts20

July 2022 1 32 Report

Срочно!!! Буду очень благодарна

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zhenyaM2002

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$\frac{6}{x^2 - 36 } - \frac{3}{x^2 - 6x} + \frac{x-12}{x^2+ 6x} = 0 \\ \\ 
 \frac{6}{x^2 - 6^2 } - \frac{3}{x(x- 6)} + \frac{x-12}{x(x+6)} = 0 \\ \\ 
\frac{6}{(x-6)(x+6)} - \frac{3}{x(x- 6)} + \frac{x-12}{x(x+6)} = 0 \\ \\ 
 \frac{6x -3(x+6) +(x-12)(x-6)}{x(x-6)(x+6)} =0 \\ \\ 
 \frac{6x -3x-18+x^2-6x-12x+72}{x(x-6)(x+6) } =0 \\ \\ 
 \frac{x^2 -15x +54}{x(x-6)(x+6)} = 0$
знаменатель ≠ 0 ⇒ х≠0 ; х≠6 ; х≠ -6
х² - 15х + 54 = 0
D = (-15)² - 4*1*54 = 225 -216=9 =3²
D>0 два корня уравнения
х₁ = (15 - 3)/ (2*1) = 12/2 = 6 ( но ! х≠6 )
х₂ = (15 +3)/2 = 18/2 = 9
Ответ: х = 9 .

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