Posted by KC on .
use a graphing utility to solve each equation, rounded to 2 decimal places
1. x^2 - 2sin2x = 3x
2. x^2 = x + 3cos2x
I don't have a graphing utility. If you don't either, use a hand calculator and iterate until you get x close enough to satsfying the equation. x=0 is one solution of the first equation. There is anotherin the vicinity of x=3.
If x = 3, x^2 - 2 sin 2x - 3x = 0.558
If x = 2.9, x^2 - 2 sin 2x - 3x = 0.174
If x = 2.8, x^2 - 2 sin 2x - 3x = 0.071
If x = 2.7, x^2 - 2 sin 2x - 3x = -0.037
If x = 2.74 x^2 - 2 sin 2x - 3x = 0.007
Try x = 2.73. You can get closer by further iteration and interpolating
Use a similar method to solve the other equation