If ab = 10, and \(a^2 + b^2 = 30\), solve for y in the equation, \(y = (a+ b)^2\).
\(y = (a+ b)^2\). Expanding the equation results in \(y = (a^2 + b^2 + 2ab)\). You know that \(a^2 + b^2 = 30\), and ab = 10. When you substitute these known values into the equation, you get y = 30 + 2(10). Solving for y, results in y = 50.