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Positive real numbers $r,s$ satisfy the equations $r^2 + s^2 = 1$ and $r^4 + s^4= \frac{7}{8}$. Find $rs$.

 Feb 1, 2015

Best Answer 

 #2
avatar+128474 
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r^2 + s^2 = 1     square both sides

r^4 + 2(rs)^2 + s^4 = 1

r^4 + s^4 = 1 - 2(rs)^2

(7/8) = 1  - 2(rs)^2   rearrange

2(rs)^2  = 1 - 7/8

2(rs)^2 = 1/8    divide both sides by 2

(rs)^2 = 2/ 16 = 1/8   take the square root of both sides

(rs) = ±√(1/8) = ±√(1/2√2) = ±√2/4

And since r and s are positive real numbers, take the positive root

 

 Feb 1, 2015
 #1
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PLEASE HELP ME! I REALLY NEED HELP!!!!!!!!!!!!!!  o_o

 

(>_<)  ($_$)  (*_*)  (^_^)  (@_@)  (:|)

 Feb 1, 2015
 #2
avatar+128474 
+5
Best Answer

r^2 + s^2 = 1     square both sides

r^4 + 2(rs)^2 + s^4 = 1

r^4 + s^4 = 1 - 2(rs)^2

(7/8) = 1  - 2(rs)^2   rearrange

2(rs)^2  = 1 - 7/8

2(rs)^2 = 1/8    divide both sides by 2

(rs)^2 = 2/ 16 = 1/8   take the square root of both sides

(rs) = ±√(1/8) = ±√(1/2√2) = ±√2/4

And since r and s are positive real numbers, take the positive root

 

CPhill Feb 1, 2015

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