x2y=75
x^2y=75
2xy + x^2 y' = 0
y' = -2xy/y^2 = -2x/y
To solve the equation x^2y = 75, you need to isolate for y.
Step 1: Divide both sides of the equation by x^2 to get y by itself:
x^2y / x^2 = 75 / x^2
This simplifies to:
y = 75 / x^2
So the solution for y in terms of x is y = 75 / x^2.
To find the values of x and y that satisfy the equation x^2y = 75, we can use algebraic methods.
Step 1: Rearrange the equation in terms of one variable.
Divide both sides of the equation by y:
x^2 = 75/y
Step 2: Solve for x.
Take the square root of both sides to eliminate the square:
x = ±√(75/y)
Step 3: Simplify the expression for x.
x = ±√(75/y) can be simplified further if we determine the value of y.
Let's consider different values of y:
Case 1: y ≠ 0
If y is any nonzero real number, then y can be a positive or negative value.
If y > 0:
x = √(75/y)
x can be any positive real number.
If y < 0:
x = -√(75/y)
x can be any negative real number.
Case 2: y = 0
If y is equal to 0, then the equation x^2y = 75 is not satisfied since any number multiplied by 0 is always 0.
Therefore, the solution to the equation x^2y = 75 depends on the value of y. If y is nonzero, then x can be any positive or negative real number. If y is equal to 0, there are no solutions.