perplexus.info :: Just Math : Real Value Validation

Real Value Validation (Posted on 2015-02-01)

Each of X, Y and Z is a real number that satisfies both of these equations:
X + Y = 2, and:
X*Y - Z² = 1

Find the value of X⁵ + Y⁵ + Z⁵

No Solution Yet Submitted by K Sengupta

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Quick and dirty (spoiler)

| Comment 1 of 3

If x + y = 2, then the maximum value of xy is when x = y = 1.

So xy <=1

So z^2 = xy - 1 <= 0

So z must be 0 and x and y must be 1.

x^5 + y^5 + z^5 = 2

Posted by Steve Herman on 2015-02-01 10:58:41

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