Question

1/x+1/z+1/y=1 решите пожалуйста поскорей

Answer 1

$\frac{1}{x}+\frac{1}{z}+\frac{1}{y}-1=0;\\\frac{yz}{xyz}+\frac{xy}{xyz}+\frac{xz}{xyz}-\frac{xyz}{xyz}=0;\\\frac{yz+xy+xz-xyz}{xyz}=0;\\yz+xy+xz-xyz=0; xyz\neq 0;$

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Answer 2

Solving the Equation 1/x + 1/z + 1/y = 1

To solve the equation 1/x + 1/z + 1/y = 1, we can use the following approach:

1. Identify the Variables: The equation contains three variables: x, y, and z. 2. Find a Common Denominator: To simplify the equation, we can find a common denominator for the fractions. 3. Solve for the Variables: Once we have a common denominator, we can solve for the variables x, y, and z.

Let's proceed with solving the equation step by step.

Finding a Common Denominator

The common denominator for the fractions 1/x, 1/z, and 1/y is the product of x, y, and z. Therefore, the common denominator is xyz.

Simplifying the Equation

By multiplying each term by the common denominator xyz, we can simplify the equation to:

yz + xz + xy = xyz

Solving for the Variables

To solve for the variables x, y, and z, we can rearrange the equation into a quadratic equation and then solve for the roots using the quadratic formula.

The quadratic equation derived from the given equation is:

xy + xz + yz - xyz = 0

This equation can be solved for the roots of x, y, and z using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Where a, b, and c are the coefficients of the quadratic equation.

By solving for the roots of x, y, and z, we can find the solutions to the given equation.

Conclusion

In conclusion, the equation 1/x + 1/z + 1/y = 1 can be solved by finding a common denominator, simplifying the equation, and then solving for the variables x, y, and z using the quadratic formula.