Question

If x² + y² = 100 and xy = 18, what is x - y?

Answer 1

To solve for x - y given that x² + y² = 100 and xy = 18, we express y in terms of x, substitute into the first equation to form a quadratic equation, and then solve for x and y to find x - y.

Step-by-step explanation:

The student asked for the solution to the problem where x² + y² = 100 and xy = 18, and we need to find x - y. To solve, we use the system of equations and manipulate the formulas. Starting with the two given equations, we know that:

• x² + y² = 100
• xy = 18

From the second equation, we can express one variable in terms of the other, for example, y = 18/x. By substituting into the first equation, we have x² + (18/x)² = 100, which simplifies to x² + 324/x² = 100. To solve for x, we'll need to manipulate this into a quadratic equation:

(x²)2 - 100x² + 324 = 0

Now, we use the quadratic formula to solve for the possible values of x². Once we have the values of x², we can find corresponding values of y using the equation xy = 18, and then calculate x - y.