Question

9n4 - 9n2 + 2 = 0
equação biquadrada, cálculo pfvr

Answer 1

Assumindo n² = t , temos :

9t² - 9t + 2 = 0

Δ = b²-4ac

Δ = (9)² - 4 · 9 · 2

Δ = 81 - 72

Δ = 9

Considere Δ = $\alpha$ ( Limitações do Brainly )

$t1 = \frac{-b+\sqrt{\alpha } }{2a}$

$t1 = \frac{9+3}{18}$

$t1 = \frac{12}{18}$

$t1 = \frac{2}{3}$

$t2 = \frac{-b - \sqrt{\alpha } }{2a}$

$t2 = \frac{9-3}{18}$

$t2 = \frac{6}{18}$

$t2 = \frac{1}{3}$

Substituindo em n² = t

n² = t1

n = $\sqrt{\frac{2}{3} }$ ou  n = $- \sqrt{\frac{2}{3} }$

n² = t2

n = $\frac{1}{\sqrt{3} }$ · $\frac{\sqrt{3} }{\sqrt{3} }$ = $\frac{\sqrt{3} }{3}$

ou

n = $- \frac{1}{\sqrt{3} }$ = $- \frac{\sqrt{3} }{3}$

δ = { $\sqrt{\frac{2}{3} } , - \sqrt{\frac{2}{3} } , \frac{\sqrt{3} }{3} , - \frac{\sqrt{3} }{3}$ }