Question

equações biquadradas
a)x²-10x²+9=0
b)-4x⁴-3x²+1=0
c)4x⁴-17x+4=0
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Answer 1

x^4 - 10x^2 + 9 = 0

y^2 - 10y + 9 = 0

delta d = 100 - 36 = 64

as raizes em y:

y1 = (10 + 8)/2 = 9

y2 =(10 - 8)/2 = 1

as raizes em x:

x1 = -3, x2 = 3, x3 = -1 , x4 = 1

-4x⁴-3x²+1=0

4y^2 + 3y - 1 = 0

delta

d = 9 + 16 = 25

as raizes em y

y1 = (-3 + 5)/8 = 1/4

y2 = (-3 - 5)/8 = -1 (nao serve)

as raizes em x;

x1 = -1/2, x2 = 1/2  

4x⁴- 17x^2 +4=0

4y^2 - 17y + 4 = 0

delta

d = 289 - 64 = 225

as raizes em y:

y1 = (17 + 15)/8 = 4

y2 = (17 - 15)/8 = 1/4

as raizes em x:

x1 = -2, x2 = 2, x3 = -1/2 , x4 = 1/2