Question

The general solution of the equation 2cos2x=3.2cos²x-4 is?

Answer 1

No real solution.

Explanation:

`2cos2x=3.2cos^2 x -4`
`2cos2x=16/5cos^2 x-4|-(16/5cos^2 x-4)`
`2cos2x-16/5cos^2(x)+4=0|* 5/2`
`5cos2x-8cos^2(x)+10=0`
`color(blue)(cos(2x)=2cos^2(x)-1)`
`5 * (color(blue)(2cos^2(x)-1))-8cos^2(x)+10=0`
`2cos^2(x)+5=0`
`cos^2(x)=-5/2`
`cos(x)=sqrt(-5/2)`
There is no real solution since the radicand is negative.