Question

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

Is this true or false

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

Answer 1

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

Answer 2

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

Answer 3

TY