In Example 2, change the + before the 7x² to − and then solve the equation.

Data from Example 2

Solve the equation 2x⁴ + 7x² = 4.
We first let y = x² to write the equation in quadratic form. We will then solve the resulting quadratic equation for y. However, solutions for x are required, so we again let y = x² to solve for x.

We can let y₁ =  2x⁴ + 7x² and y₂ = 4  to solve the system on a calculator. The display is shown in Fig. 14.15, and we see that there are two points of intersection, one for x = 0.7071 (shown on screen) and the other for x = −0.7071 (not shown). Because 1/√2 = 0.7071, this verifies the real solutions. The imaginary solutions cannot be found graphically. Substitution of each value in the original equation shows each value to be a solution.

Transcribed Image Text:

2y2 + 7y4 = 0 (2y 1)(y + 4) = 0 y = 1/ x² = 1/ - : ++/2 x = + or y = -4 or x² = -4 or x = +2j let y = x² factor and solve for y y = x² (to solve for x)