SOLUTION: My problem is the following: {{{x^2+xy+y^2=9}}} Could you help me isolate y? My work so far is: {{{(y+3x)*(y-2x)=-7x^2+9}}}

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: My problem is the following: {{{x^2+xy+y^2=9}}} Could you help me isolate y? My work so far is: {{{(y+3x)*(y-2x)=-7x^2+9}}}      Log On


   



Question 507175: My problem is the following:
x%5E2%2Bxy%2By%5E2=9
Could you help me isolate y?
My work so far is:
%28y%2B3x%29%2A%28y-2x%29=-7x%5E2%2B9

Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
What you did was mathematically correct but it doesn't help
isolate y.

    x² + xy + y² = 9

First get 0 on the right

x² + xy + y² - 9 = 0

Rearrange in descending powers of y:

y² + xy + x² - 9 = 0 

Think of it as a quadratic equation in y this way:

1y^2 + xy + (x²-9) = 0

Then use the quadratic formula 

y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a = 1, b = x, c = (x²-9)



y+=+%28-x+%2B-+sqrt%28x%5E2-4%28x%5E2-9%29%29%29%2F2+

y+=+%28-x+%2B-+sqrt%28x%5E2-4x%5E2%2B36%29%29%2F2+

y+=+%28-x+%2B-+sqrt%28-3x%5E2%2B36%29%29%2F2+

y+=+%28-x+%2B-+sqrt%2836-3x%5E2%29%29%2F2+

Edwin