Answer :
Answer:
To find the general solution of the equation x^2 * p * y^2 * q = (x*y)^z, we need to solve for x, y, and z in terms of p and q. Let's approach this step by step.
Given:
x^2 * p * y^2 * q = (x*y)^z
Step 1: Simplify the right-hand side of the equation using the properties of exponents.
(x*y)^z = x^z * y^z
Step 2: Rewrite the equation using the simplified right-hand side.
x^2 * p * y^2 * q = x^z * y^z
Step 3: Equate the exponents of x and y on both sides of the equation.
For x: 2 = z
For y: 2 = z
Since the exponents of x and y are equal, we can conclude that z = 2.
Step 4: Substitute z = 2 into the equation and simplify.
x^2 * p * y^2 * q = x^2 * y^2
p * q = 1
Therefore, the general solution of the equation x^2 * p * y^2 * q = (x*y)^z is:
z = 2
p * q = 1
This means that for any values of x and y, the equation will hold true as long as z equals 2 and the product of p and q equals 1.
