What is the answer to 2(x^2+2)=5sqrt(x^3+1) ?

The answer to 2(x^2+2)=5sqrt(x^3+1) is x\approx-0.54138…,x\approx 5.54138…

Solve for x: 2(x^2+2)=5sqrt(x^3+1)

The solution is x\approx-0.54138…,x\approx 5.54138…

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2 (x^{2} + 2) = 5 x^{3} + 1

x \approx - 0.54138 \dots, x \approx 5.54138 \dots

Solution steps

2 (x^{2} + 2) = 5 x^{3} + 1

Expand

2 (x^{2} + 2) : 2 x^{2} + 4

2 x^{2} + 4 = 5 x^{3} + 1

Square both sides:

4 x^{4} + 16 x^{2} + 16 = 25 x^{3} + 25

4 x^{4} + 16 x^{2} + 16 = 25 x^{3} + 25

Solve

4 x^{4} + 16 x^{2} + 16 = 25 x^{3} + 25 : x \approx - 0.54138 \dots, x \approx 5.54138 \dots

x \approx - 0.54138 \dots, x \approx 5.54138 \dots

Verify Solutions:

x \approx - 0.54138 \dots

True

, x \approx 5.54138 \dots

True

The solutions are

x \approx - 0.54138 \dots, x \approx 5.54138 \dots

x^{\frac{1}{2}} + 3 x - 3 = 4

4 - \frac{4}{x ^{\frac{1}{3}}} = 0

5 = x + 1

What is the answer to 2(x^2+2)=5sqrt(x^3+1) ?
The answer to 2(x^2+2)=5sqrt(x^3+1) is x\approx-0.54138…,x\approx 5.54138…
Solve for x: 2(x^2+2)=5sqrt(x^3+1)
The solution is x\approx-0.54138…,x\approx 5.54138…