Question

Помогите пожалуйста!
Решите уравнение. ​

Answer 1

а)

$\displaystyle \tt \frac{x^2}{x^2-64}=\frac{3x+40}{x^2-64}\: \: \: \: \: | \: x\ne-8, \: x\ne8\\x^2=3x+40\\x^2-3x-40=0\\x^2+5x-8x-40=0\\x(x+5)-8(x+5)=0\\(x+5)(x-8)=0\\x+5=0\\x_1=-5\\x-8=0\\x_2=8$

Ответ: $x_1=-5$

б)

$\displaystyle \tt \frac{20}{x-1}-\frac{6}{x}=3 \: \: \: \: \: | \: x\ne1, \: x\ne0\\\frac{20}{x-1}-\frac{6}{x}-3=0\\\frac{20x-6(x-1)-3x(x-1)}{x(x-1)}=0\\\frac{20x-6x+6-3x^2+3x}{x(x-1)}=0\\\frac{17x+6-3x^2}{x(x-1)}=0\\17x+6-3x^2=0\\-3x^2+17x+6=0\\3x^2-17x-6=0\\3x^2+x-18x-6=0\\x(3x+1)-6(3x+1)=0\\(3x+1)(x-6)=0\\3x+1=0\\3x=-1\\x_1=-\frac{1}{3}\\x-6=0\\x_2=6$

Ответ: $x_1=-\frac{1}{3}; \: x_2=6$