( 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 )
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( 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 )