What are the solutions to the equation r^4-2r^2+1=0 ?

The solutions to the equation r^4-2r^2+1=0 are r=1,r=-1

Find the zeros of r^4-2r^2+1=0

The zeros of r^4-2r^2+1=0 are r=1,r=-1

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r^{4} - 2 r^{2} + 1 = 0

r = 1, r = - 1

Solution steps

r^{4} - 2 r^{2} + 1 = 0

Rewrite the equation with

u = r^{2}

and

u^{2} = r^{4}

u^{2} - 2 u + 1 = 0

Solve

u^{2} - 2 u + 1 = 0 : u = 1

u = 1

Substitute back

u = r^{2},

solve for

r

Solve

r^{2} = 1 : r = 1, r = - 1

The solutions are

r = 1, r = - 1

x^{3} - 4 x - 2 = 1

x^{3} - 1 = 1

(x^{2} - 5)^{2} - 3 (x^{2} - 5) = 4

x^{4} - x^{3} - 1 = 0

m^{3} = \frac{8}{27}

What are the solutions to the equation r^4-2r^2+1=0 ?
The solutions to the equation r^4-2r^2+1=0 are r=1,r=-1
Find the zeros of r^4-2r^2+1=0
The zeros of r^4-2r^2+1=0 are r=1,r=-1