For all real numbers a and b, 2a • b = a2 + b2

Is this true or false

False
a=1, b=2=>4=5 false

I confused myself I studied about it and I got it thanks.

TY

To determine if the statement is true or false, we can use counterexamples. A counterexample is a specific example or set of values that satisfy the given conditions and produce a result that does not match the given equation.

In this case, we can find a counterexample by choosing specific values for a and b that make the equation false. The given equation is:

2a • b = a^2 + b^2

Let's try a = 1 and b = 2:

2(1) • 2 = (1^2) + (2^2)
2 • 2 = 1 + 4
4 = 5

Since 4 does not equal 5, we have found a counterexample where the equation does not hold true. Therefore, the statement is false.

a ^ 2 + b ^ 2 = a ^ 2 + 2 a * b + b ^ 2

2 a * b = a ^ 2 + b ^ 2

2 a * b = a ^ 2 + 2 a * b + b ^ 2 Subtract 2 a * b to both sides

2 a * b - 2 a * b = a ^ 2 + 2 a * b + b ^ 2 - 2 a * b

0 = a ^ 2 + b ^ 2 Subtract a ^ 2 to both sides

0 - a ^ 2 = a ^ 2 + b ^ 2 -a ^ 2

- a ^ 2 = b ^ 2

Negative square of a ^ 2 can't be identic with positive b ^ 2.

Obviously false.

This is true only if a = b becouse :

If a = b

2 a * b = a ^ 2 + b ^ 2

2 a * a = a ^ 2 + a ^ 2

2 a ^ 2 = 2 a ^ 2

But in this case a and b is not different numbers.

Answer:

False