Given: alpha - beta = 8 and alpha2 + beta2 = 74.

April 7, 2026Mathematics

ScanSolve AI Answer

April 7, 2026

Answer

8 $and$ \alpha^2 + \beta^2 = 74$.

Here's a step-by-step solution to each problem:

: Quadratic Equation Roots Given: $\alpha - \beta = 8$ and $\alpha^2 + \beta^2 = 74$ . We need to find a quadratic equation with integer coefficients whose roots are $r_1 = 2\alpha + \beta$ and $r_2 = 2\beta + \alpha$ .

Step 1: Find $\alpha\beta$ . We know that $(\alpha - \beta)^2 = \alpha^2 - 2\alpha\beta + \beta^2$ . Substitute the given values: $8^2 = 74 - 2\alpha\beta$ $64 = 74 -

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Quick Answer

Here's a step-by-step solution to each problem: Problem 1: Quadratic Equation Roots Given: - = 8 and ^2 + ^2 = 74.

Asked on April 7, 2026Mathematics

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 AnswerAnswered on April 7, 2026

Here's a step-by-step solution to each problem: Problem 1: Quadratic Equation Roots Given: - = 8 and ^2 + ^2 = 74. We need to find a quadratic equation with integer coefficients whose roots are r_1 = 2 + and r_2 = 2 + . Step 1: Find . We know that ( - )^2 = ^2 - 2 + ^2. Substitute the given values: 8^2 = 74 - 2 $64 = 74 -