What are the solutions to the equation 9x^4-47x^2+10=0 ?

The solutions to the equation 9x^4-47x^2+10=0 are x=sqrt(5),x=-sqrt(5),x=(sqrt(2))/3 ,x=-(sqrt(2))/3

Find the zeros of 9x^4-47x^2+10=0

The zeros of 9x^4-47x^2+10=0 are x=sqrt(5),x=-sqrt(5),x=(sqrt(2))/3 ,x=-(sqrt(2))/3

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9 x^{4} - 47 x^{2} + 10 = 0

x = 5, x = - 5, x = \frac{2}{3}, x = - \frac{2}{3}

Decimal Notation

x = 2.23606 \dots, x = - 2.23606 \dots, x = 0.47140 \dots, x = - 0.47140 \dots

Solution steps

9 x^{4} - 47 x^{2} + 10 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

9 u^{2} - 47 u + 10 = 0

Solve

9 u^{2} - 47 u + 10 = 0 : u = 5, u = \frac{2}{9}

u = 5, u = \frac{2}{9}

Substitute back

u = x^{2},

solve for

x

Solve

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

Solve

x^{2} = \frac{2}{9} : x = \frac{2}{3}, x = - \frac{2}{3}

The solutions are

x = 5, x = - 5, x = \frac{2}{3}, x = - \frac{2}{3}

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

4 x^{3} - 6 x + 1 = 0

125 x^{3} = 64

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

8 y^{3} - 125 = 0

What are the solutions to the equation 9x^4-47x^2+10=0 ?
The solutions to the equation 9x^4-47x^2+10=0 are x=sqrt(5),x=-sqrt(5),x=(sqrt(2))/3 ,x=-(sqrt(2))/3
Find the zeros of 9x^4-47x^2+10=0
The zeros of 9x^4-47x^2+10=0 are x=sqrt(5),x=-sqrt(5),x=(sqrt(2))/3 ,x=-(sqrt(2))/3