Question

Помогите решить подробно

(x/(x-1))^2+(x/(x+1))^2=45/16

Answer 1

$frac{x^2}{(x-1)^2}+frac{x^2}{(x+1)^2}=frac{45}{16}\frac{x^2(x+1)^2+x^2(x-1)^2}{(x-1)^2(x+1)^2}=frac{45}{16}\frac{x^2((x+1)^2+(x-1)^2)}{(x-1)^2(x+1)^2}=frac{45}{16}\frac{x^2(2x^2+2)}{x^4-2x^2+1}=frac{45}{16}\16x^2(2x^2+2)=45(x^4-2x^2+1)\32x^4+32x^2=45x^4-90x^2+45\13x^4-122x^2+45=0\x^2=t\13t^2-122t+45=0\D=14884-4*13*45=12544\t_{_1}=frac{5}{13}\t_{_2}=9\\1)x^2=t\x^2=frac{5}{13}\x=бsqrt{frac{5}{13}}\2)x^2=t\x^2=9\x=б3$

 

Answer 2

(x^2*(x+1)^2+x^2*(x-1)^2)/((x-1)^2*(x+1)^2)=45/16
(x^2((x+1)^2+(x-1)^2))/(x^2-1)^2=45/16
(x^2(2x^2 + 2))/(x^4-2x^2+1) = 45/16
32x^4+32x^2=45x^4-90x^2+45
13x^4-122x^2+45=0        Замена: x^2=y 
13y^2-122y+45=0
D/4=3721-585=56^2
y=117/13            y=5/13
x^2=117/13        x^2=5/13
x= +/-корень из 117/13 
x=+/-корень из 5/13