What are the solutions to the equation n^5+100=n^1+5^5 ?

The solutions to the equation n^5+100=n^1+5^5 are n\approx 4.96921…

Find the zeros of n^5+100=n^1+5^5

The zeros of n^5+100=n^1+5^5 are n\approx 4.96921…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

n^{5} + 100 = n^{1} + 5^{5}

n \approx 4.96921 \dots

Solution steps

n^{5} + 100 = n^{1} + 5^{5}

Expand

n^{1} + 5^{5} : n + 3125

n^{5} + 100 = n + 3125

Move

3125

to the left side

n^{5} - 3025 = n

Move

n

to the left side

n^{5} - 3025 - n = 0

Write in the standard form

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

n^{5} - n - 3025 = 0

Find one solution for

n^{5} - n - 3025 = 0

using Newton-Raphson:

n \approx 4.96921 \dots

Apply long division:

\frac{n ^{5} - n - 3025}{n - 4.96921 \dots} = n^{4} + 4.96921 \dots n^{3} + 24.69308 \dots n^{2} + 122.70518 \dots n + 608.74826 \dots

n^{4} + 4.96921 \dots n^{3} + 24.69308 \dots n^{2} + 122.70518 \dots n + 608.74826 \dots \approx 0

Find one solution for

n^{4} + 4.96921 \dots n^{3} + 24.69308 \dots n^{2} + 122.70518 \dots n + 608.74826 \dots = 0

using Newton-Raphson:

No Solution for

n \in R

The solution is

n \approx 4.96921 \dots

x^{3} \cdot 13 = x^{2} \cdot 247

(2 x - 9) (x^{2} - 4) = 0

x^{3} - 4 x^{2} - 5 x = 0

x - x^{3} = 1

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

What are the solutions to the equation n^5+100=n^1+5^5 ?
The solutions to the equation n^5+100=n^1+5^5 are n\approx 4.96921…
Find the zeros of n^5+100=n^1+5^5
The zeros of n^5+100=n^1+5^5 are n\approx 4.96921…