Question

As raízes da equação x°4-11x°2+18=0

Answer 1

Equação biquadrada

$x^4-11x^2+18=0$

Usar o artifício x² =y

y² -11x +18=0

a=1

b=-11

c=18

Δ=b²-4ac

Δ=(-11)²-4(1)(18)

Δ=121-72

Δ=49

$y={-b\pm\sqrt{\Delta} \over2a}={-(-11)\pm\sqrt{49} \over2(1)}={11\pm7\over2}\\ \\ y'={11+7\over2}={18\over2}=9\\ \\ y"={11-7\over2}={4\over2}=2\\ \\ como\\ x^2=y\\ x^2=9\\ x=\pm\sqrt{9} \\ \\ x=\pm3\\ \\ e\\ x^2=2\\ x=\pm\sqrt{2}\\ \\ S=\{\pm3,\pm\sqrt{2} \}$