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
________________________________________
Remark :
x ^ 2 + 2 x + 1 = ( x + 1 ) ^ 2
________________________________________
( 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
Related Questions
Algebra - Could you please check my work. Determine whether the realtion is a ...
College Algebra - 1.Answer the following for the given quadratic function. f(x...
Precalc - In this function, f(x)= [2/(x-3)]+1: I know it is a rational function ...
Algebra 2 - Describe the end behavior of the graph of the polynomial function. ...
trig/precalc - a car's flywheel has a timing mark on it's outer edge. ...
Algebra 2 - Describe the end behavior of the graph of the polynomial function. ...
Calculus - Find a linear function whose graph is the plane that intersects the ...
Calculus - Find a linear function whose graph is the plane that intersects the ...
Calculus - Find a linear function whose graph is the plane that intersects the ...
trig - Graph three periods of the function. (identify period and phase shift and...
For Further Reading
