Question

Show that ( y=x² eˣ) is a solution to the equation ( y-={x yˣ). Please note that you're not being asked to solve this, but to write a sequence of statements that

Answer 1

To show that y = x²eˣ is a solution to the equation y = x^yˣ, substitute the expression for y into the equation and simplify to prove their equality.

Step-by-step explanation:

To show that y = x²eˣ is a solution to the equation y = x^yˣ, we need to substitute the expression for y into the equation and verify that the equation holds true. Let's go through the steps:

1. Replace y in the equation with x²eˣ to obtain x²eˣ = x^(x²eˣ)ˣ.
2. Simplify both sides of the equation:
3. After the simplification, we see that the left side of the equation is the same as the right side: x²eˣ = x^(2xeˣ)ˣ. Therefore, y = x²eˣ is indeed a solution to the equation y = x^yˣ.

Thus, we have shown that y = x²eˣ satisfies the given equation.