What are the solutions to the equation y^4-6y^2=-5 ?

The solutions to the equation y^4-6y^2=-5 are y=sqrt(5),y=-sqrt(5),y=1,y=-1

Find the zeros of y^4-6y^2=-5

The zeros of y^4-6y^2=-5 are y=sqrt(5),y=-sqrt(5),y=1,y=-1

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y^{4} - 6 y^{2} = - 5

y = 5, y = - 5, y = 1, y = - 1

Decimal

y = 2.23606 \dots, y = - 2.23606 \dots, y = 1, y = - 1

Solution steps

y^{4} - 6 y^{2} = - 5

Move

5

to the left side

y^{4} - 6 y^{2} + 5 = 0

Rewrite the equation with

u = y^{2}

and

u^{2} = y^{4}

u^{2} - 6 u + 5 = 0

Solve

u^{2} - 6 u + 5 = 0 : u = 5, u = 1

u = 5, u = 1

Substitute back

u = y^{2},

solve for

y

Solve

y^{2} = 5 : y = 5, y = - 5

Solve

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

The solutions are

y = 5, y = - 5, y = 1, y = - 1

x^{3} + 5 x^{2} = 4 x + 20

x^{4} + 62 x^{2} + 128 x + 65

a^{4} + a^{3} + a^{2} + a + 1 = 0

x^{4} - 113 x^{2} + 3136 = 0

x^{4} - 3 x^{3} - 5 x^{2} + 6 x - 8

What are the solutions to the equation y^4-6y^2=-5 ?
The solutions to the equation y^4-6y^2=-5 are y=sqrt(5),y=-sqrt(5),y=1,y=-1
Find the zeros of y^4-6y^2=-5
The zeros of y^4-6y^2=-5 are y=sqrt(5),y=-sqrt(5),y=1,y=-1