Question

resolva as equaçoes
a) x⁴-16x²=0
b) 11x⁴-7x²-4=0
c)4x⁴-5x²+9=0
d)x⁴-8x²= -15
e)x⁴+36-20x²=0

Answer 1

a) Vamos supor que x²=K
( x²)²-16x²=0
K²-16K=0

Delta=b²-4ac
=(-16)²-4×1×0
=256

K(I)=-b+ √Delta / 2a
K(I)=16+ √256/2×1
K(I)= 16+16/2
K(I)= 32/2
K(I)= 16

K(II)=-b- √Delta / 2a
K(II)= 16- √256/2×1
K(II)= 16-16/2
K(II)= 0/2
K(II)= 0

x²= K(I)
x²=16
x= √16
x=-4 ou +4 (I)

x²= K (II)
x²=0
x= √0
x=0

S={-4; 4}

b) x²=J
11 ( x²)²-7x²-4=0
11J²-7J-4=0

Delta= b²- 4ac
=(-7)²-4×11×(-4)
=49-4×(-44)
=49+176
=225

J(I)=-b+ √Delta / 2a
J(I)=7+ √225/2×11
J(I)=7+15/22
J(I)=22/22
J(I)=1

J(II)=-b- √Delta / 2a
J(II)=7- √225/2×11
J(II)=7-15/22
J(II)=8/22
J(II)=4/11

x²= J (I)
x²=1
x= √1
x=-1 ou +1

x²=J (II)
x²= 4/11
x= √4/11
x= -2 √1/11 ou +2 √1/11

S={1; -1; -2 √1/11; +2 √1/11}

c) x²=L
4 ( x²)²-5 x²+9=0
4L²-5L+9=0

Delta= (-5)²-4×4×9
= 25-144
= -119

S= VAZIA

d) x²=M
(x²)²-8 x²=-15
M²-8M=-15
M²-8M+15=0

Delta= (-8) ²-4×1×15
=64-60
=4

M (I)= 8+ √4 / 2×1
M (I)= 8+2/2
M (I)= 10/2
M (I)= 5

M (II)= 8- √4/2×1
M (II)= 8-2/2
M (II)= 6/2
M (II)= 3

x²= M(I)
x²= 5
x= √5
x=-√5 ou +√5

x²= M (II)
x²= 3
x= √3
x=-√3 ou +√3

S={- √3; + √3; - √5; + √5}

e) x²=N
(x²)²+36-20x²=0
N²-20N+36=0

Delta= (-20)²-4×1×36
= 400-144
= 256

N (I)= 20+ √256/2×1
N (I)= 20+16/2
N (I)= 36/2
N (I)= 18

N (II)= 20- √256/2×1
N (II)= 20-16/2
N (II)= 4/2
N (II)= 2

x²= N (I)
x²= 18
x= √18
x=-3 √2 ou +3 √2

x²= N (II)
x²= 2
x= √2
x=- √2 ou + √2

S={-3√2; +3√2; -√2; +√2}