Question

Find all the solutions to .5x^4-5x^2+2=0

Thanks

Answer 1

5x⁴ -5x² + 2 = 0

It have four roots

put x² = t then The equation becomes

5t² - 5t + 2 = 0

This is a quadratic equation form

Therefore the roots of the equation : t1 =[ -b +√(b² - 4ac)] / 2a and t2 = [-b - √(b² - 4ac)] / 2a

Substitute a = 5 , b= -5 and c = 2 in the roots t1, t2

t1 = [5 + √(25 - 4(10))] / 2(5) and t2 = 5 - √(25 - 4(10))] / 2(5)

t1 = 5 + √(-15) / 10 and t2 = 5 - √(-15) / 10

Substitute  -1 =i²  in the above roots t1 , t2

t1 = [5+ i√(15)] / 10 and t2 = 5 - i√(15)] / 10

but t1 = x1² and t2 = x2² then the four  roots are x1, x3, x2 , x4

x1 = √[(5+i√(15)) / 10] , x3 = -√[(5+i√(15)) / 10] , x2 = √5 - i√(15)) / 10] and x4 = -√[(5 - i√(15)) / 10].

Answer 2

I hope it helps a lil