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Ответ:
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1)x^4-10x^2 заменим на y
y^2-2y-99=0
D = b^2 - 4ac = (-2)2 - 4·1·(-99) = 4 + 396 = 400
y1 = (2 - √400) / (2·1) = (2 - 20)/ 2 = -18/2 = -9
y2 = (2 + √400) / (2·1) = (2 + 20)/ 2 = 22/2 = 11
2) x^4-10x^2=-9 x^4 = z^2 ; x^2 = z
z^2-10z=-9
D = b^2 - 4ac = (-10)2 - 4·1·9 = 100 - 36 = 64
x1 = (10 - √64) / (2·1) = (10 - 8) / 2 = 2/2 = 1
x2 = (10 + √64) / (2·1) = (10 + 8) / 2 = 18/2 = 9
x^2= 1; -1
X^2= -3; 3
3)x^4-10x^2=11
x^4= t^2; x^2=t
t^2-10t-11=0
D = b^2 - 4ac = (-10)2 - 4·1·(-11) = 100 + 44 = 144
t1 = (10 - √144) / 2·1 = (10 - 12) / 2 = -2/2 = -1
t2 = (10 + √144) / 2·1 = (10 + 12) / 2 = 22/2 = 11
x^2= x∉R
x^2 =
Відповідь: x1=x∉R, x2=-3, x3=-1, x4=1, x5=3, x6=
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