What is the answer to ψ/(ψ^2+1)=sqrt(1-ψ) ?

The answer to ψ/(ψ^2+1)=sqrt(1-ψ) is ψ\approx 0.76682…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

ψ/(ψ^2+1)=sqrt(1-ψ)

\frac{ψ}{ψ ^{2} + 1} = 1 - ψ

ψ \approx 0.76682 \dots

Solution steps

\frac{ψ}{ψ ^{2} + 1} = 1 - ψ

Multiply both sides by

ψ^{2} + 1

\frac{ψ}{ψ ^{2} + 1} (ψ^{2} + 1) = 1 - ψ (ψ^{2} + 1)

Simplify

ψ = 1 - ψ (ψ^{2} + 1)

Expand

1 - ψ (ψ^{2} + 1) : 1 - ψ ψ^{2} + 1 - ψ

ψ = 1 - ψ ψ^{2} + 1 - ψ

Factor

1 - ψ ψ^{2} + 1 - ψ : (ψ^{2} + 1) 1 - ψ

ψ = (ψ^{2} + 1) 1 - ψ

Square both sides:

ψ^{2} = ψ^{4} - ψ^{5} + 2 ψ^{2} - 2 ψ^{3} + 1 - ψ

ψ^{2} = ψ^{4} - ψ^{5} + 2 ψ^{2} - 2 ψ^{3} + 1 - ψ

Solve

ψ^{2} = ψ^{4} - ψ^{5} + 2 ψ^{2} - 2 ψ^{3} + 1 - ψ : ψ \approx 0.76682 \dots

ψ \approx 0.76682 \dots

Verify Solutions:

ψ \approx 0.76682 \dots

True

The solution is

ψ \approx 0.76682 \dots

55 = \frac{143}{1 x}

18 = 3 (2)^{0.5} X^{0.5}

- 2 x + 9 = 22

x + 6 - 4 = x

x^{2} + 64 = 10

What is the answer to ψ/(ψ^2+1)=sqrt(1-ψ) ?
The answer to ψ/(ψ^2+1)=sqrt(1-ψ) is ψ\approx 0.76682…
Solve for ψ: ψ/(ψ^2+1)=sqrt(1-ψ)
The solution is ψ\approx 0.76682…