1) t =((3- 2x)/(5x+1))² ;
t = 82/9 - 1/t ;
t +1/t = 82/9 ; **** [ t² - 82/9t +1 =0] ***
t +1/t =9 +1/9 ;
[ t =9 ; t =1/9.
a) ((3- 2x)/(5x+1))² =9 .
[(3- 2x)/(5x+1) = - 3 ;(3- 2x)/(5x+1) = 3 . [ x = -6/13 ;x =0.
b) ((3- 2x)/(5x+1))² =1/9.
[(3- 2x)/(5x+1) = -1/ 3 ;(3- 2x)/(5x+1) = 1/3. [ x = 10 ; x =8/11.
ответ : - 6/13 ;0 ; 8/11 ;10.
2) (x/(x-1))² + (x/(x +1))² =45/16;
(x/(x -1) + x/(x+1))² - 2*x/(x-1)*x/(x+1) =45/16 ;
(2x²/(x² -1))² -2x²/(x² -1) =45/16 ;
t =2x²/(x² -1);
t² - t -45/16 =0;
t₁ = -5/4 ;
t₂ = 9/4 .
a) 2x²/(x² -1) = -5/4 не имеет решения ю
b) 2x²/(x² -1) = 9/4 ⇒ x ₁= - 3 ; x₂ =3;
ответ : - 3 ;3 .
------------------------------- или ---------------------------
(1+1/(x-1))² + (1 - 1/(x+1))² =45/16 ;
. . .
B6=b1*q^5
b1=b6/q^5=3/3^5=3/243=1/81
( х + 6 )( х + 5 ) = х^2 + 5х + 6х + 30 = х^2 + 11х + 30
5/6х+ 1 2/3=2х-3
1 2/3+3=2х-5/6х
4 2/3=1 1/6х
Х=4 2/3:1 1/6
Х=4.
Ответ: 4.
0,376;3/8;4/11;-1,6;-5 5/3;-5,(8)