This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the given quadratic equation and its roots. The quadratic equation is x^2 - 4x + 2 = 0. The roots are and . Step 2: Use Vieta's formulas to find the sum and product of the roots. For a quadratic equation ax^2 + bx + c = 0, the sum of the roots is + = -(b)/(a) and the product of the roots is = (c)/(a). In this equation, a=1, b=-4, and c=2. + = -(-4)/(1) = 4 = (2)/(1) = 2 Step 3: Simplify the expression (1)/() + (1)/(). To add these fractions, find a common denominator: (1)/() + (1)/() = ()/() + ()/() = ( + )/() Step 4: Substitute the values of + and into the simplified expression. ( + )/() = (4)/(2) = 2 The value of (1)/() + (1)/() is 2. The final answer is 2.