Question

For all real numbers a and b, 2a • b = a2 + b2.
True or False ? Explain.

Answer 1

False. You can pick any two numbers, but not the same number, to show its false. try it

Answer 2

Real number is the total of all numbers. The equation $2a \cdot b = a^2 + b^2$ is false.

Given

$2a \cdot b = a^2 + b^2$

To prove or disprove the above equation, we simply assume values for a and b.

Assume that:

$a=5$

$b = 6.7$

The equation becomes:

$2 \times 5 \times 6.7 = 5^2 + 6.7^2$

$67 = 25 + 44.89$

$67 = 68.89$

The above equation is false

i.e. $67 \ne 68.89$

This means that: $2a \cdot b = a^2 + b^2$ is false

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