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If x, y and z are positive real numbers such that √x + √y - √z is the positive square root of 21 - 4√5 + 8√3 - 4√15, what is the value of xyz?

Question

If x, y and z are positive real numbers such that √x + √y - √z is the positive square root of 21 - 4√5 + 8√3 - 4√15, what is the value of xyz?
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Solution 1

To solve the problem, we need to simplify the expression 21−45+83−415 \sqrt{21 - 4\sqrt{5} + 8\sqrt{3} - 4\sqrt{15}} and then find the values of x x , y y , and z z such that x+y−z \sqrt{x} + \sqrt{y} - \sqrt{z} equals this simplified expression. Finally, we will calculate xyz xyz .

Step 1:

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Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
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