Given alpha - beta = 5 and alpha beta = 7, find the value of alpha2 + beta2.

Question

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The initial statement about α, β being roots of x² − α x + β = 0 is inconsistent with the given conditions α − β = 5 and α β = 7. We will proceed by using the given conditions to find α² + β². Step 1: Identify the given values. We are given: α − β = 5; α β = 7 Step 2: Use an algebraic identity. We know the algebraic identity for the square of a difference: (α − β)² = α² − 2α β + β² Step 3: Rearrange the identity to solve for α² + β². Add 2α β to both sides of the identity: α² + β² = (α − β)² + 2α β Step 4: Substitute the given values into the rearranged identity. Substitute α − β = 5 and α β = 7: α² + β² = (5)² + 2(7) Step 5: Calculate the final value. α² + β² = 25 + 14; α² + β² = 39 The value of α² + β² is 39.

Given alpha − beta = 5 and alpha beta = 7, find the value of alpha2 + beta2.

Answer

Step-by-step solution

Identify the given values.

Use an algebraic identity.

Rearrange the identity to solve for $\alpha^2 + \beta^2$ .

Substitute the given values into the rearranged identity.

Calculate the final value.

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