2 xsquare y -3 xsquare+ 4 y=2010
2x^2y - 3x^2 + 4y = 2010
y(2x^2+4) = 2010 + 3x^2
y = (2010+3x^2)/(2x^2+4)
= 3/2 + 1002/(x^2+2)
now what?
To solve the equation 2x^2y - 3x^2 + 4y = 2010, we need to rearrange it and simplify it to a more standard form.
First, let's rewrite the equation:
2x^2y - 3x^2 + 4y = 2010
Next, let's try to isolate one variable, either x or y. We can start by grouping the terms containing y together:
2x^2y + 4y - 3x^2 = 2010
Now, factor out the common terms:
y(2x^2 + 4) - 3x^2 = 2010
We can simplify this equation further by factoring out 2 from the first term:
2y(x^2 + 2) - 3x^2 = 2010
Now, rearrange the terms:
2y(x^2 + 2) = 3x^2 + 2010
To solve for either x or y, we need to know the value of the other variable. Let's solve for x in terms of y or y in terms of x.
Let's isolate x by dividing both sides of the equation by (3x^2 + 2010):
2y(x^2 + 2) / (3x^2 + 2010) = 1
Now, we can solve for x by taking the square root of both sides:
x = ± √[(2y / (3 + 2010/x^2)]
Similarly, if we want to solve for y, we can rearrange the equation:
2y(x^2 + 2) = 3x^2 + 2010
2y = (3x^2 + 2010) / (x^2 + 2)
y = (3x^2 + 2010) / (2(x^2 + 2))
Now you have the equations to solve for x or y, depending on which variable you know the value for.