Question

Quais são as raízes da equação x4 -20x2 + 36 = 0

Answer 1

x⁴ - 20x² + 36 = 0

=> b/c= -20/+36 = -18 - 2 / -18 • -2

(x² -18). (x² -2) = 0

x²=18.…x²=2

x=√18...x=±√2

x=±3√2...x=±√2 ✓

Answer 2

X^4 -20x^2 +36
substituindo x^2 por Z

Z^2 -20Z+36=0

Delta=b^2 -4ac=(-20)^2 -4*1*36=400-144=256

Delta^(1/2)=16

Z1=-b+16/2a=20+16/2=36/2=18
Z2=20-16/2=4/2=2


como x^2=Z

Z1=x^2
X^2=18
x=+/-(18)^(1/2)=+/-3*2^(1/2)

Z2=x^2
x^2=2
x=+/- 2^(1/2)

Então as raizes são 3*2^(1/2) ,-3*2^(1/2),2^(1/2),-2^(1/2)