What is the answer to -sqrt(x^3)-4sqrt(x)+4x+1=0 ?

The answer to -sqrt(x^3)-4sqrt(x)+4x+1=0 is x=1,x=0.14589…,x=6.85410…

Solve for x: -sqrt(x^3)-4sqrt(x)+4x+1=0

The solution is x=1,x=0.14589…,x=6.85410…

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- x^{3} - 4 x + 4 x + 1 = 0

x = 1, x = 0.14589 \dots, x = 6.85410 \dots

Solution steps

- x^{3} - 4 x + 4 x + 1 = 0

Use the following exponent property

x^{3} = (x)^{(3 \cdot 2)}

- (x)^{6} - 4 x + 4 (x)^{2} + 1 = 0

Rewrite the equation with

x = u

- u^{6} - 4 u + 4 u^{2} + 1 = 0

Solve

- u^{6} - 4 u + 4 u^{2} + 1 = 0 : u = 1, u \approx 0.38196 \dots, u \approx 2.61803 \dots, u \approx - 4.86453 \dots

u = 1, u \approx 0.38196 \dots, u \approx 2.61803 \dots, u \approx - 4.86453 \dots

Substitute back

u = x,

solve for

x

Solve

x = 1 : x = 1

Solve

x = 0.38196 \dots : x = 0.14589 \dots

Solve

x = 2.61803 \dots : x = 6.85410 \dots

Solve

x = - 4.86453 \dots :

No Solution for

x \in R

x = 1, x = 0.14589 \dots, x = 6.85410 \dots

Verify Solutions:

x = 1

True

, x = 0.14589 \dots

True

, x = 6.85410 \dots

True

The solutions are

x = 1, x = 0.14589 \dots, x = 6.85410 \dots

20 - x = x - 8

an s

\frac{3 x + 16}{2 x + 8} = 0

4 x + 4 = x + 1

x + 3 = 21

What is the answer to -sqrt(x^3)-4sqrt(x)+4x+1=0 ?
The answer to -sqrt(x^3)-4sqrt(x)+4x+1=0 is x=1,x=0.14589…,x=6.85410…
Solve for x: -sqrt(x^3)-4sqrt(x)+4x+1=0
The solution is x=1,x=0.14589…,x=6.85410…