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Positive real numbers x and y satisfy the equations x^2 + y^2 = 1 and x^4 + y^4 = 5/8. Find xy.

 Oct 21, 2021
 #1
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answer: sqrt(3)

 Oct 21, 2021
 #2
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Hello Guest,

 

there are 5 solutions, but one of them have positive real numbers.

 

\((x,y)=(\frac{1}{2},\frac{\sqrt{3}}{2})\) \(\mbox {wolframalpha}\)

 

\(\frac{1}{2}*\frac{\sqrt{3}}{2}= \mbox { } \approx {0.433}\) .

 

Straight

 Oct 30, 2021
 #3
avatar+32738 
+2

You can do it like this:

 Oct 31, 2021

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