Question

2*Sqrt[x]-x^(1/4)=1 Помогите, пожалуйста

Answer 1

$2* \sqrt{x} - \sqrt[4]{x} =1$
Пусть $\sqrt[4]{x} =t$, тогда получаем
2t²-t-1=0
D=9
t1=-0,5; t2=1
$\sqrt[4]{x}=-0,5$ ⇒ x1=0.0625 и
$\sqrt[4]{x}=1$ ⇒ x2=1

Answer 2

Solving the Equation 2*Sqrt[x] - x^(1/4) = 1

To solve the equation 2*Sqrt[x] - x^(1/4) = 1, we can follow these steps:

1. Let's first isolate the square root term by adding x^(1/4) to both sides of the equation: 2*Sqrt[x] = x^(1/4) + 1

2. Now, we can square both sides of the equation to eliminate the square root: (2*Sqrt[x])^2 = (x^(1/4) + 1)^2

3. Simplify the equation: 4*x = x^(1/2) + 2*x^(1/4) + 1

4. Rearrange the terms to form a quadratic equation: 4*x - x^(1/2) - 2*x^(1/4) - 1 = 0

5. Now, we can solve this quadratic equation to find the value of x.

Solution to the Equation

The solution to the equation 2*Sqrt[x] - x^(1/4) = 1 involves solving a quadratic equation derived from the given equation. The specific steps to solve the quadratic equation and find the value of x are as follows:

1. Substitute y = x^(1/4) to simplify the equation: 4*y^4 - 2*y^2 - 4*y + 1 = 0

2. This is a quartic equation in terms of y. We can solve for y using appropriate methods for quartic equations.

3. Once we find the value(s) of y, we can substitute back x = y^4 to obtain the corresponding values of x.

Conclusion

The solution to the equation 2*Sqrt[x] - x^(1/4) = 1 involves solving a quartic equation to find the values of x that satisfy the given equation. The specific steps for solving the quartic equation and obtaining the values of x have been outlined above.

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