Question

Resolva a seguinte equação biquadrada: (x² - 1)² + (x² - 3)² = 10

Answer 1

Explicação passo-a-passo:

$\sf (x^2-1)^2+(x^2-3)^2=10$

$\sf x^4-2x^2+1+x^4-6x^2+9=10$

$\sf 2x^4-8x^2+10=10$

$\sf 2x^4-8x^2+10-10=0$

$\sf 2x^4-8x^2=0$

$\sf 2x^2\cdot(x^2-4)=0$

• $\sf 2x^2=0$

$\sf x^2=\dfrac{0}{2}$

$\sf x^2=0$

$\sf x=\pm\sqrt{0}$

$\sf x_1=x_2=0$

• $\sf x^2-4=0$

$\sf x^2=4$

$\sf x=\pm\sqrt{4}$

• $\sf x_3=2$

• $\sf x_4=-2$

$\sf S=\{-2,0,2\}$