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Find the number of ordered triples (x,y,z) of real numbers that satisfy the system of equation: x y z = 7; x^2 y^2 z^2 = 27; xyz = 5 ?
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Find the number of ordered triples (x,y,z) of real numbers that satisf...
Solution:

Let's solve the given system of equations step by step.

Equation 1: x * y * z = 7

Equation 2: x^2 * y^2 * z^2 = 27

Equation 3: x * y * z = 5

Step 1: Solve for z in terms of x and y using Equation 1 and Equation 3.

From Equation 1, we have z = 7 / (x * y).

Substituting this value of z in Equation 3, we get:

x * y * (7 / (x * y)) = 5

Simplifying the above equation, we have:

7 = 5

This equation is not possible since 7 is not equal to 5. Hence, there are no real solutions for x, y, and z that satisfy the given system of equations.

Conclusion: There are no ordered triples (x, y, z) of real numbers that satisfy the given system of equations.
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Find the number of ordered triples (x,y,z) of real numbers that satisfy the system of equation: x y z = 7; x^2 y^2 z^2 = 27; xyz = 5 ?
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Find the number of ordered triples (x,y,z) of real numbers that satisfy the system of equation: x y z = 7; x^2 y^2 z^2 = 27; xyz = 5 ? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Find the number of ordered triples (x,y,z) of real numbers that satisfy the system of equation: x y z = 7; x^2 y^2 z^2 = 27; xyz = 5 ? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the number of ordered triples (x,y,z) of real numbers that satisfy the system of equation: x y z = 7; x^2 y^2 z^2 = 27; xyz = 5 ?.
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