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# Algebra

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70
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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
0

Oct 21, 2021
#2
+390
0

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
+32738
+2

You can do it like this:

Oct 31, 2021