Question

The assessment for this lesson is a discussion of a mathematical statement. You will have to determine if the statement is true or false. If it is false, you will explain your reasoning. For all real numbers a and b, 2a • b = a2 + b2

Answer 1

2 a ∙ b = a² + b²

Subtract 2 a ∙ b to both sides

2 a ∙ b - 2 a ∙ b = a² + b² - 2 a ∙ b

0 = a² + b² - 2 a ∙ b

a² + b² - 2 a ∙ b = 0

a² - 2 a ∙ b + b² = 0

( a - b )² = 0

Take the square of both sides

a - b = 0

Add b to both sides

a - b + b = 0 + b

a = b

The statement is true if a = b