What are the solutions to the equation 16x^4=15(x+1)^4 ?

The solutions to the equation 16x^4=15(x+1)^4 are x\approx-0.49596…,x\approx 61.47983…

Find the zeros of 16x^4=15(x+1)^4

The zeros of 16x^4=15(x+1)^4 are x\approx-0.49596…,x\approx 61.47983…

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16 x^{4} = 15 (x + 1)^{4}

x \approx - 0.49596 \dots, x \approx 61.47983 \dots

Solution steps

16 x^{4} = 15 (x + 1)^{4}

Expand

15 (x + 1)^{4} : 15 x^{4} + 60 x^{3} + 90 x^{2} + 60 x + 15

16 x^{4} = 15 x^{4} + 60 x^{3} + 90 x^{2} + 60 x + 15

Switch sides

15 x^{4} + 60 x^{3} + 90 x^{2} + 60 x + 15 = 16 x^{4}

Move

16 x^{4}

to the left side

- x^{4} + 60 x^{3} + 90 x^{2} + 60 x + 15 = 0

Find one solution for

- x^{4} + 60 x^{3} + 90 x^{2} + 60 x + 15 = 0

using Newton-Raphson:

x \approx - 0.49596 \dots

Apply long division:

\frac{- x ^{4} + 60 x ^{3} + 90 x ^{2} + 60 x + 15}{x + 0.49596 \dots} = - x^{3} + 60.49596 \dots x^{2} + 59.99603 \dots x + 30.24398 \dots

- x^{3} + 60.49596 \dots x^{2} + 59.99603 \dots x + 30.24398 \dots \approx 0

Find one solution for

- x^{3} + 60.49596 \dots x^{2} + 59.99603 \dots x + 30.24398 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

x \approx 61.47983 \dots

The solutions are

x \approx - 0.49596 \dots, x \approx 61.47983 \dots

x^{4} + x^{3} + 23 x^{2} + 25 x - 50 = 0

(p) = p^{3} + 1

t^{4} - t^{2} - 2 = 0

x, 171 y = 3 x^{5}

(x^{2} - 4) (x - 2) = 0

What are the solutions to the equation 16x^4=15(x+1)^4 ?
The solutions to the equation 16x^4=15(x+1)^4 are x\approx-0.49596…,x\approx 61.47983…
Find the zeros of 16x^4=15(x+1)^4
The zeros of 16x^4=15(x+1)^4 are x\approx-0.49596…,x\approx 61.47983…