Asked by Anonymous
Calculate solution set.
x^2+4y^2=68
xy=8
x^2+4y^2=68
xy=8
Answers
Answered by
Damon
y = 8/x
x^2 + 4 (64/x^2) = 68
x^4 - 68 x^2 + 256 = 0
let z = x^2
z^2 -68 x + 256 = 0
(z-64)(z-4) = 0
z = 64 or 4
so
x = 2 or -2 or 8 or -8
if x = 2, y = 4
if x = -2, y = -4
if x = 8, y = 1
if x = -8, y = -1
x^2 + 4 (64/x^2) = 68
x^4 - 68 x^2 + 256 = 0
let z = x^2
z^2 -68 x + 256 = 0
(z-64)(z-4) = 0
z = 64 or 4
so
x = 2 or -2 or 8 or -8
if x = 2, y = 4
if x = -2, y = -4
if x = 8, y = 1
if x = -8, y = -1
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