Question

Resolva as equações biquadrada
X elevado a 4-3 x ao quadrado igual a 4 e Y elevado a 4 - 5 y ao quadrado menos 36 igual a 0

Answer 1

a) $x^{4}-3x^2=4 \\ ( x^{2} )^2-3x^2-4=0 \\ y^2-3y-4=0$

Δ= $(-3)^{2}-4*1*(-4)$
Δ= $9+6$
Δ= $25$

x= -b +- √Δ÷ 2×a
$x= \frac{-(-3)+- \sqrt{25} }{2*1} \\ x= \frac{3+-5}{2} \\ x'= \frac{3+5}{2}= \frac{8}{2}= 4 \\ x''= \frac{3-5}{2}= \frac{-2}{2}= -1$

b) $(y^{2})^2- 5y^{2}-36=0 \\ y^2-5y-36=0$

Δ= $(-5)^2-4*1*(-36)$
Δ= $25+144$
Δ= $169$

$x= \frac{-(-5)+- \sqrt{169} }{2*1} \\ x= \frac{5+-13}{2} \\ x'= \frac{5+13}{2}= \frac{18}{2}= 9 \\ x''=\frac{5-13}{2}= \frac{-8}{2}= -4$