What is the answer to (x^3-1)/(sqrt(x)-1)=5.5 ?

The answer to (x^3-1)/(sqrt(x)-1)=5.5 is x\approx 0.93138…

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(x^3-1)/(sqrt(x)-1)=5.5

\frac{x ^{3} - 1}{x - 1} = 5.5

x \approx 0.93138 \dots

Solution steps

\frac{x ^{3} - 1}{x - 1} = 5.5

Multiply both sides by

x - 1

\frac{x ^{3} - 1}{x - 1} (x - 1) = 5.5 (x - 1)

Simplify

x^{3} - 1 = 5.5 (x - 1)

Expand

5.5 (x - 1) : 5.5 x - 5.5

x^{3} - 1 = 5.5 x - 5.5

Remove square roots

x^{6} + 9 x^{3} + 20.25 = 30.25 x

Solve

x^{6} + 9 x^{3} + 20.25 = 30.25 x : x = 1, x \approx 0.93138 \dots

x = 1, x \approx 0.93138 \dots

Verify Solutions:

x = 1

False

, x \approx 0.93138 \dots

True

The solution is

x \approx 0.93138 \dots

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5 x = 15

9 - 9 x = x + 9

x, u = x^{0.5} + y

6 x - 7 x - 3 = 0

What is the answer to (x^3-1)/(sqrt(x)-1)=5.5 ?
The answer to (x^3-1)/(sqrt(x)-1)=5.5 is x\approx 0.93138…
Solve for x: (x^3-1)/(sqrt(x)-1)=5.5
The solution is x\approx 0.93138…