Posted by Matt on Thursday, October 4, 2012 at 8:53pm.
x ^ 2 - x y + 2 x - 1 = 0 Add xy to both sides
x ^ 2 - x y + 2 x - 1 + x y = 0 + x y
x ^ 2 + 2 x - 1 = x y
Roots :
When y = 0 then :
x ^ 2 + 2 x - 1 = x * 0
x ^ 2 + 2 x - 1 = 0 Add 2 to both sides
x ^ 2 + 2 x - 1 + 2 = 0 + 2
x ^ 2 + 2 x + 1 = 2
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Remark :
x ^ 2 + 2 x + 1 = ( x + 1 ) ^ 2
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( x + 1 ) ^ 2 = 2 Take the square root of both sides
x + 1 = + OR - sqrt ( 2 ) Subtract 1 to both sides
x + 1 - 1 = + OR - sqrt ( 2 ) - 1
x = + OR - sqrt ( 2 ) - 1
x1 = sqrt ( 2 ) - 1 = approx 0.41
x2 = - sqrt ( 2 ) - 1 = approx. - 2.41
Revrite x ^ 2 + 2 x - 1 = x y
Divide both sides by x
x ^ 2 / x + 2 x / x - 1 / x = x y / x
x + 2 - 1 / x = y
y = x - 1 / x + 2
for x = 0
x - 1 / x + 2 -> + OR - infinity
Go on wolfram alpha dot com
When page be open in rectangle type :
plot x ^ 2 - x y + 2 x - 1 = 0
and click option =
You will see graph