Решите уравнения, используя замену неизвестного. (x2-x)^2 - 3(x2-x)+2=0 (x2-10x)^2+8(x-5)^2-209=0

( х^2 - Х )^2 - 3( х^2 - Х ) + 2 = 0 Х^2 - Х = а а^2 - 3а + 2 = 0 D = 9 - 8 = 1 a1 = ( 3 + 1 ) : 2 = 2 a2 = ( 3 - 1 ) : 2 = 1 X^2 - x = a X^2 - x = 2 X^2 - x - 2 = 0 D = 1 + 8 = 9 = 3^2 X1 = ( 1 + 3 ) : 2 = 2 X2 = ( 1 - 3 ) : 2 = - 1 X^2 - x - 1 = 0 D = 1 + 4 = 5 = ( V 5 )^2 Х1 = ( 1 + V5 ) : 2 = 0,5 + 0,5V5 X2 = 0,5 - 0,5V5 ОТВЕТ 2 ; - 1 ; ( 0,5 + 0,5V5 ) ; ( 0,5 - 0,5V5 ) ========== ( x^2 - 10x )^2 + 8( x - 5 )^2 - 209 = 0 ( x - 5 )^2 = x^2 - 10x + 25 X^2 - 10x = a X^2 - 10x + 25 = a + 25 a^2 + 8( a + 25 ) - 209 = 0 a^2 + 8a + 200 - 209 = 0 a^2 + 8a - 9 = 0 D = 64 + 36 = 100 = 10^2 a1 = ( - 8 + 10 ) : 2 = 1 a2 = ( - 8 - 10 ) : 2 = - 9 X^2 - 10x = 1 X^2 - 10x - 1 = 0 D = 100 + 4 = 104 = ( V100•1,04 )^2 = ( 10V1,04)^2 X1 = ( 10 + 10V1,04 ) : 2 = 5 + 5V1,04 X2 = 5 - 5V1,04 X^2 - 10x = - 9 X^2 - 10x + 9 = 0 D = 100 - 36 = 64 = 8^2 X1 = ( 10 + 8 ) : 2 = 9 X2 = ( 10 - 8 ) : 2 = 1 ОТВЕТ 9 ; 1 ; ( 5 + 5V1,04 ) ; ( 5 - 5V1,04 )