What are the solutions to the equation x^4-8x^2+15=0 ?

The solutions to the equation x^4-8x^2+15=0 are x=sqrt(5),x=-sqrt(5),x=sqrt(3),x=-sqrt(3)

Find the zeros of x^4-8x^2+15=0

The zeros of x^4-8x^2+15=0 are x=sqrt(5),x=-sqrt(5),x=sqrt(3),x=-sqrt(3)

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x^{4} - 8 x^{2} + 15 = 0

x = 5, x = - 5, x = 3, x = - 3

Decimal Notation

x = 2.23606 \dots, x = - 2.23606 \dots, x = 1.73205 \dots, x = - 1.73205 \dots

Solution steps

x^{4} - 8 x^{2} + 15 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} - 8 u + 15 = 0

Solve

u^{2} - 8 u + 15 = 0 : u = 5, u = 3

u = 5, u = 3

Substitute back

u = x^{2},

solve for

x

Solve

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

Solve

x^{2} = 3 : x = 3, x = - 3

The solutions are

x = 5, x = - 5, x = 3, x = - 3

r^{5} - 5 r = 3

9 x^{4} = 25 x^{2} - 16

x, x^{3} + y^{3} - z^{3} = 4

x^{3} - 2 x - 5 = 0, (x = 2.0813)

(x - \frac{1}{3}) (x^{2} + x \frac{0.1}{3} + \frac{1 ^{2}}{3 ^{2}}) = 64

What are the solutions to the equation x^4-8x^2+15=0 ?
The solutions to the equation x^4-8x^2+15=0 are x=sqrt(5),x=-sqrt(5),x=sqrt(3),x=-sqrt(3)
Find the zeros of x^4-8x^2+15=0
The zeros of x^4-8x^2+15=0 are x=sqrt(5),x=-sqrt(5),x=sqrt(3),x=-sqrt(3)