+0  
 
0
90
1
avatar

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

 Apr 17, 2021
 #1
avatar+121004 
+1

x^2 +y^2  =  1

 

Square  both sides

 

x^4  +  2(xy)^2  + y^4   =  1

 

Subbing  in  we  have

 

5/8  +  2(xy)^2  =  1

 

2(xy)^2   =  1  - 5/8

 

2(xy)^2  =  3/8

 

(xy)^2   = 3/16

 

xy  =   sqrt (3)  / 4      

 

cool cool cool

 Apr 17, 2021

10 Online Users

avatar
avatar