Step-by-step explanation:
To find the value of 3x + 5y, we can use the given equations:
1. 9x² + 25y² = 181
2. xy = -6
First, we need to find the values of x and y. Let's solve for x and y using the second equation:
xy = -6
Substitute y = -6/x into the first equation:
9x² + 25(-6/x)² = 181
9x² + 25(36/x²) = 181
9x² + 900/x² = 181
9x^4 + 900 = 181x²
9x^4 - 181x² + 900 = 0
This is a quadratic equation in terms of x. Solve for x using the quadratic formula.
Once you have found the values of x and y, substitute them into 3x + 5y to find the final answer. If you need further assistance with the calculations or solving the quadratic equation, feel free to ask!
