Question

Solve the following equations.

a) x^3 + x = 4x^2 - 6

b) 3x^4 - 5x^2 + 2 = 0

Answer 1

a) $x^3+x=4x^2−6$

Step 1: Subtract $4x^2-6$ from both sides.

$x^3+x−(4x^2−6)=4x^2−6−(4x^2−6)$

$x^3−4x^2+x+6=0$

Step 2: Factor left side of equation.

$(x+1)(x−2)(x−3)=0$

Step 3: Set factors equal to 0.

$x+1=0$  or $x−2=0$  or $x−3=0$

$x=−1$  or $x=2$ or $x=3$

b) $3x^4 - 5x^2 + 2 = 0$

Step 1: Factor left side of equation.

$(x+1)(x−1)(3x^2−2)=0$

Step 2: Set factors equal to 0.

$x+1=0$ or $x−1=0$  or $3x^2−2$ =0

$x=−1$  or $x=1$ or $x=0.816496581$  or $x=−0.816496581$