# Show that the roots of the equation #16x^4 - 20x^2 + 5= 0# are #cos((kx)/10) #for #k = 1,3,7 # and # 9# And Deduce that #cos^2(pi/10)cos^2((3pi)/10) = 5/16#?

##### 2 Answers

Antoine, I think that your roots are without

To solve your equation substitute

Your roots corresponds to

and if you have:

Has real zeroes, because

For the full solution, see Gio's answer.)

The factor theorem gives us:

The constant for this product is clearly

Therefore,

**For the first part**

Expand

Then with

In fact, with