Question

4x⁴- 17x²+4=0


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Answer 1

Olá.

4x⁴- 17x²+4=0

x²= u

4u²-17u+4=0

a= 4 b=-17 c=4

Δ= b²-4ac

Δ= (-17)² -4·4·4

Δ= 289 - 64

Δ= 225

u= -b +/- √Δ

          2a

u= 17 +/-√225

          2·4

u= 17+/-15

        8

u'= 17+15 =  4

          8

u''= 17-15=  2 = 1

         8         8     4

S:[1/4 ,4]

u=x²

logo u= {1/4 ,4}

1/4= x²

x'= √1/4

x'= + 1/2 , -1/2

4=x²

x=√4

x= +2, -2

S:{ +1/2, -1/2,+2,-2}

Answer 2

4x⁴ - 17x² + 4 = 0

4.(x²)² - 17(x²) + 4 = 0

x² = y

4y² - 17y + 4 = 0

a = 4; b = - 17; c = 4  

Δ = b² - 4ac

Δ = (-17)² - 4.4.4

Δ = 289 - 64

Δ = 225

y = - b +/- √Δ = - (-17) +/- √225

         2a                 2.4

y = 17 + 15 = 32/8 = 4

          8

y = 17 - 15 = 2 (:2)  =  1 x² = y

x² = 4

x = √4

x = + 2 e x = - 2

x² = y

x² = 1

     4

x = √1/4

x = +1/2 e x = - 1/2

R.: (-2, +2, 1/2, - 1/2)