Question

Como resolver esta equação biquadrada: (x²-2)²+(x²-4)²=0​

Answer 1

Resposta:

$(a-b)^2=a^2-2ab+b^2$

$(x^2-2)^2+(x^2-4)^2=0<=>$

$<=>x^4-4x^2+4+x^4-8x^2+16=0<=>$

$<=>2x^4-12x^2+20=0<=>$

$<=>2(x^4-6x^2+10)=0<=>$

$<=>x^4-6x^2+10=\frac{0}{2} <=>$

$x^2=y$

$<=>y^2-6y+10=0<=$$>$

Formula resolvente

$<=>y=\frac{6+-\sqrt{36-4*1*10} }{2*1} <=>$

$<=>y=\frac{6+-\sqrt{-4} }{2} <=>$

$<=>x^2=y<=>$

$<=>x^2=\frac{6+-\sqrt{-4} }{2} <=>$

$<=>x=+-\sqrt{\frac{6+-\sqrt{-4} }{2} }$

ou

$<=>x=+-\sqrt{3+-i}$