What are the solutions to the equation 64a^6-112a^4+56a^2-7=0 ?

The solutions to the equation 64a^6-112a^4+56a^2-7=0 are

Find the zeros of 64a^6-112a^4+56a^2-7=0

The zeros of 64a^6-112a^4+56a^2-7=0 are

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64 a^{6} - 112 a^{4} + 56 a^{2} - 7 = 0

a = \frac{2.35319 E 15}{1.25 E 16}, a = - \frac{2.35319 E 15}{1.25 E 16}, a = \frac{3.0563 E 15}{5.0 E 15}, a = - \frac{3.0563 E 15}{5.0 E 15}, a = \frac{2.97026 E 14}{3.125 E 14}, a = - \frac{2.97026 E 14}{3.125 E 14}

Decimal Notation

a = 0.43388 \dots, a = - 0.43388 \dots, a = 0.78183 \dots, a = - 0.78183 \dots, a = 0.97492 \dots, a = - 0.97492 \dots

Solution steps

64 a^{6} - 112 a^{4} + 56 a^{2} - 7 = 0

Rewrite the equation with

u = a^{2}, u^{2} = a^{4}

and

u^{3} = a^{6}

64 u^{3} - 112 u^{2} + 56 u - 7 = 0

Solve

64 u^{3} - 112 u^{2} + 56 u - 7 = 0 : u \approx 0.18825 \dots, u \approx 0.61126 \dots, u \approx 0.95048 \dots

u \approx 0.18825 \dots, u \approx 0.61126 \dots, u \approx 0.95048 \dots

Substitute back

u = a^{2},

solve for

a

Solve

a^{2} = 0.18825 \dots : a = \frac{2.35319 E 15}{1.25 E 16}, a = - \frac{2.35319 E 15}{1.25 E 16}

Solve

a^{2} = 0.61126 \dots : a = \frac{3.0563 E 15}{5.0 E 15}, a = - \frac{3.0563 E 15}{5.0 E 15}

Solve

a^{2} = 0.95048 \dots : a = \frac{2.97026 E 14}{3.125 E 14}, a = - \frac{2.97026 E 14}{3.125 E 14}

The solutions are

a = \frac{2.35319 E 15}{1.25 E 16}, a = - \frac{2.35319 E 15}{1.25 E 16}, a = \frac{3.0563 E 15}{5.0 E 15}, a = - \frac{3.0563 E 15}{5.0 E 15}, a = \frac{2.97026 E 14}{3.125 E 14}, a = - \frac{2.97026 E 14}{3.125 E 14}

4 x^{2} + 8 x^{4} = (x^{2} + 2 x + 1)

4 x^{3} - 27 x^{2} - 11 x - 1 = 0

(1 - m)^{3} = \frac{1}{3}

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

4 x^{3} - 54 x^{2} + 180 x - 125 = 0

What are the solutions to the equation 64a^6-112a^4+56a^2-7=0 ?
The solutions to the equation 64a^6-112a^4+56a^2-7=0 are
Find the zeros of 64a^6-112a^4+56a^2-7=0
The zeros of 64a^6-112a^4+56a^2-7=0 are