<PRE><B>Question 104027</B>
x^2 + y^2 = 16
y^2 = 16 - x^2
y = {{{sqrt(16-x^2)}}}
:
xy = 8
substitute {{{sqrt(16-x^2)}}}for y, find x:
x*{{{sqrt(16-x^2)}}} = 8
Square both sides
x^2(16-x^2) = 64
:
-x^4 + 16x^2 - 64 = 0; a quadratic equation
+x^4 - 16x^2 + 64 = 0; multiplied by -1
Factor:
(x^2 - 8)(x^2 - 8) = 0
x^2 = +8
x = {{{sqrt(8)}}}
x = {{{2sqrt(2)}}}
:
Find y:
{{{2sqrt(2)}}}*y = 8
y = {{{8/(2sqrt(2))}}}
y = {{{4/sqrt(2)}}}



(x + y)^2 = ?
FOIL
({{{2sqrt(2)}}}+{{{4/sqrt(2)}}})*({{{2sqrt(2)}}}+{{{4/sqrt(2)}}}) = ?
4(2) + {{{8sqrt(2)/sqrt(2)}}} + {{{8sqrt(2)/sqrt(2)}}} + {{{16/2}}} =
 8  +  8  + 8  + 8 = 32
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