What are the solutions to the equation solvefor y,y=1.1(y^2-2)^5 ?

The solutions to the equation solvefor y,y=1.1(y^2-2)^5 are y\approx-1.00856…,y\approx 1.76028…

Find the zeros of solvefor y,y=1.1(y^2-2)^5

The zeros of solvefor y,y=1.1(y^2-2)^5 are y\approx-1.00856…,y\approx 1.76028…

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solve for

y, y = 1.1 (y^{2} - 2)^{5}

y \approx - 1.00856 \dots, y \approx 1.76028 \dots

Solution steps

y = 1.1 (y^{2} - 2)^{5}

Multiply both sides by

10

y \cdot 10 = 11 (y^{2} - 2)^{5}

Expand

11 (y^{2} - 2)^{5} : 11 y^{10} - 110 y^{8} + 440 y^{6} - 880 y^{4} + 880 y^{2} - 352

y \cdot 10 = 11 y^{10} - 110 y^{8} + 440 y^{6} - 880 y^{4} + 880 y^{2} - 352

Switch sides

11 y^{10} - 110 y^{8} + 440 y^{6} - 880 y^{4} + 880 y^{2} - 352 = y \cdot 10

Move

y 10

to the left side

11 y^{10} - 110 y^{8} + 440 y^{6} - 880 y^{4} + 880 y^{2} - 352 - y \cdot 10 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

11 y^{10} - 110 y^{8} + 440 y^{6} - 880 y^{4} + 880 y^{2} - 10 y - 352 = 0

Find one solution for

11 y^{10} - 110 y^{8} + 440 y^{6} - 880 y^{4} + 880 y^{2} - 10 y - 352 = 0

using Newton-Raphson:

y \approx - 1.00856 \dots

Apply long division:

\frac{11 y ^{10} - 110 y ^{8} + 440 y ^{6} - 880 y ^{4} + 880 y ^{2} - 10 y - 352}{y + 1.00856 \dots} = 11 y^{9} - 11.09423 \dots y^{8} - 98.81073 \dots y^{7} + 99.65718 \dots y^{6} + 339.48910 \dots y^{5} - 342.39732 \dots y^{4} - 534.66954 \dots y^{3} + 539.24977 \dots y^{2} + 336.13077 \dots y - 349.01021 \dots

11 y^{9} - 11.09423 \dots y^{8} - 98.81073 \dots y^{7} + 99.65718 \dots y^{6} + 339.48910 \dots y^{5} - 342.39732 \dots y^{4} - 534.66954 \dots y^{3} + 539.24977 \dots y^{2} + 336.13077 \dots y - 349.01021 \dots \approx 0

Find one solution for

11 y^{9} - 11.09423 \dots y^{8} - 98.81073 \dots y^{7} + 99.65718 \dots y^{6} + 339.48910 \dots y^{5} - 342.39732 \dots y^{4} - 534.66954 \dots y^{3} + 539.24977 \dots y^{2} + 336.13077 \dots y - 349.01021 \dots = 0

using Newton-Raphson:

y \approx 1.76028 \dots

Apply long division:

\frac{11 y ^{9} - 11.09423 \dots y ^{8} - 98.81073 \dots y ^{7} + 99.65718 \dots y ^{6} + 339.48910 \dots y ^{5} - 342.39732 \dots y ^{4} - 534.66954 \dots y ^{3} + 539.24977 \dots y ^{2} + 336.13077 \dots y - 349.01021 \dots}{y - 1.76028 \dots} = 11 y^{8} + 8.26888 \dots y^{7} - 84.25516 \dots y^{6} - 48.65573 \dots y^{5} + 253.84125 \dots y^{4} + 104.43509 \dots y^{3} - 350.83424 \dots y^{2} - 78.31774 \dots y + 198.26939 \dots

11 y^{8} + 8.26888 \dots y^{7} - 84.25516 \dots y^{6} - 48.65573 \dots y^{5} + 253.84125 \dots y^{4} + 104.43509 \dots y^{3} - 350.83424 \dots y^{2} - 78.31774 \dots y + 198.26939 \dots \approx 0

Find one solution for

11 y^{8} + 8.26888 \dots y^{7} - 84.25516 \dots y^{6} - 48.65573 \dots y^{5} + 253.84125 \dots y^{4} + 104.43509 \dots y^{3} - 350.83424 \dots y^{2} - 78.31774 \dots y + 198.26939 \dots = 0

using Newton-Raphson:

No Solution for

y \in R

The solutions are

y \approx - 1.00856 \dots, y \approx 1.76028 \dots

2 x^{3} - 2 x^{2} - 12 x = 0

- x^{3} + 12 x - 16 = 0

30 x^{4} + 30 x^{2} = 0

1 0^{4} = x^{4} - (x - 0.5)^{4}

4 x^{1} + 4 x^{2} + 2 x^{3} = 4

What are the solutions to the equation solvefor y,y=1.1(y^2-2)^5 ?
The solutions to the equation solvefor y,y=1.1(y^2-2)^5 are y\approx-1.00856…,y\approx 1.76028…
Find the zeros of solvefor y,y=1.1(y^2-2)^5
The zeros of solvefor y,y=1.1(y^2-2)^5 are y\approx-1.00856…,y\approx 1.76028…