[tex] \sqrt{ \frac{18-7x-x^2}{8-6x+x^2} } + \sqrt{ \frac{8-6x+x^2}{18-7x-x^2} } = \frac{13}{6} [/tex] решите уравнение пожалуйста подробно
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ОДЗ(18-7x-x²)/(8-6x+x²)>0
(x²+7x-18)/(x²-6x+8)>0
x²+7x-18=0
x1+x2=-7 U x1*x2=-18⇒x1=-9 U x2=2
x²-6x+8=0
x1+x2=6 U x1*x2=8⇒x1=2 U x2=4
(x+9)(x-2)/(x-2)(x-4)>0⇒(x+9)/(x-4)>0,x≠2
x∈(-∞;-9) U (4;∞)
√(18-7x-x²)/(8-6x+x²)=a
a+1/a=13/6
6a²-13a+6=0
D=169-144=25
a1=(13-5)/12=2/3
√(18-7x-x²)/(8-6x+x²)=2/3
(18-7x-x²)/(8-6x+x²)=4/9
162-63x-9x²=32-24x+4x²
13x²+39x-130=0
x²+3x-10=0
x1+x2=-3 U x1*x2=-10
x1=-5
x2=2∉ОДЗ
a2=(13+5)/12=3/2
√(18-7x-x²)/(8-6x+x²)=3/2
(18-7x-x²)/(8-6x+x²)=9/4
72-28x-4x²=72-54x+9x²
13x²-26x=0
13x(x-2)=0
x=0 ∉ОДЗ
х=2∉ОДЗ
Ответ х=-5