What are the solutions to the equation x^4+x^2=4x^2-2 ?

The solutions to the equation x^4+x^2=4x^2-2 are x=sqrt(2),x=-sqrt(2),x=1,x=-1

Find the zeros of x^4+x^2=4x^2-2

The zeros of x^4+x^2=4x^2-2 are x=sqrt(2),x=-sqrt(2),x=1,x=-1

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x^{4} + x^{2} = 4 x^{2} - 2

x = 2, x = - 2, x = 1, x = - 1

Decimal Notation

x = 1.41421 \dots, x = - 1.41421 \dots, x = 1, x = - 1

Solution steps

x^{4} + x^{2} = 4 x^{2} - 2

Move

2

to the left side

x^{4} + x^{2} + 2 = 4 x^{2}

Move

4 x^{2}

to the left side

x^{4} - 3 x^{2} + 2 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} - 3 u + 2 = 0

Solve

u^{2} - 3 u + 2 = 0 : u = 2, u = 1

u = 2, u = 1

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 2 : x = 2, x = - 2

Solve

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

The solutions are

x = 2, x = - 2, x = 1, x = - 1

x^{3} + 27

4 x^{3} - 24 x^{2} + 48 x = 0

9 x^{3} + 45 x^{2} + 59 x + 15

64 m = m^{3} - m^{2} + m - 62

3 x^{3} - x^{2} - 4 x = 0

What are the solutions to the equation x^4+x^2=4x^2-2 ?
The solutions to the equation x^4+x^2=4x^2-2 are x=sqrt(2),x=-sqrt(2),x=1,x=-1
Find the zeros of x^4+x^2=4x^2-2
The zeros of x^4+x^2=4x^2-2 are x=sqrt(2),x=-sqrt(2),x=1,x=-1