Question

3) Resolva em R, a equação biquadrada.
${ x}^{4} - 10x^{2} + 9 = 0$

​

Answer 1

x⁴ — 10x² + 9 =0

seja: x⁴ = t²

x² = t

t²—10t+9=0

onde:

a = 1 ; b = —10 ; b = 9

Lembrando que:

∆ = b² —4 .a.cllp

∆ = (—10)² — 4.1.9

∆ = 100 — 36

∆ = 64

t1 = (10+8)/2

t1 = 18/2

t 1 = 9

t2 = (10-8)/2

t2 = 2/2

t2 = 1

x1/2 = ±√t1

x1/2=±√9

x1,2 = ±3

x3,4 = ±√t2

x3,4 = ±√1

x3,4 = ±1

Sol: {—1,—3,1,3}