What is the answer to 7sqrt(x/((1-x)))+8sqrt(((1-x))/x)=15 ?

The answer to 7sqrt(x/((1-x)))+8sqrt(((1-x))/x)=15 is x\approx 0.50000…,x\approx 0.56637…

Solve for x: 7sqrt(x/((1-x)))+8sqrt(((1-x))/x)=15

The solution is x\approx 0.50000…,x\approx 0.56637…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

7 \frac{x}{( 1 - x )} + 8 \frac{( 1 - x )}{x} = 15

x \approx 0.50000 \dots, x \approx 0.56637 \dots

Solution steps

7 \frac{x}{( 1 - x )} + 8 \frac{( 1 - x )}{x} = 15

Remove square roots

\frac{- 6525 x ^{4} + 60510 x ^{3} - 68096 x ^{2} + 12416 x + 4096}{x ^{4} - 2 x ^{3} + x ^{2}} + 50625 = \frac{57600 ( 1 - x )}{x}

Solve

\frac{- 6525 x ^{4} + 60510 x ^{3} - 68096 x ^{2} + 12416 x + 4096}{x ^{4} - 2 x ^{3} + x ^{2}} + 50625 = \frac{57600 ( 1 - x )}{x} : x \approx 0.16350 \dots, x \approx 0.50000 \dots, x \approx 0.56637 \dots, x \approx 0.86982 \dots

x \approx 0.16350 \dots, x \approx 0.50000 \dots, x \approx 0.56637 \dots, x \approx 0.86982 \dots

Verify Solutions:

x \approx 0.16350 \dots

False

, x \approx 0.50000 \dots

True

, x \approx 0.56637 \dots

True

, x \approx 0.86982 \dots

False

The solutions are

x \approx 0.5, x \approx 0.56637 \dots

a^{\frac{1}{3}} = 2 6^{\frac{1}{3}} + 7^{\frac{1}{3}} + 6 3^{\frac{1}{3}}

x^{\frac{4}{3}} - 5 x^{\frac{2}{3}} - 36 = 0

5 + x + 14 = x + 34

3 x - 10 = 2

2 x^{2} + 5 x - 5 = 0

What is the answer to 7sqrt(x/((1-x)))+8sqrt(((1-x))/x)=15 ?
The answer to 7sqrt(x/((1-x)))+8sqrt(((1-x))/x)=15 is x\approx 0.50000…,x\approx 0.56637…
Solve for x: 7sqrt(x/((1-x)))+8sqrt(((1-x))/x)=15
The solution is x\approx 0.50000…,x\approx 0.56637…