Question

For all real numbers a and b, 2a • b = a2 + b2
Is this false or true? if its false explain.

Answer 1

@Janu16

Answer 2

hi

Answer 3

@AloneS

Answer 4

Definately false I would recommend just show a counter example by picking an a and b and checking

Answer 5

Why is it false

Answer 6

well first let me just check to make sure what you have is it this

\[2ab=a^2+b^2\]

Answer 7

yes

Answer 8

well the first is two times a times b, the second is a times a plus b times b.

Answer 9

yup

Answer 10

So for instance if a is 3 and b is 4, the first is 2*3*4 or 24 while the second is 9+16 or 25

Answer 11

yea

Answer 12

so if put any numbers in for a and b it would be wrong?

Answer 13

well not any but most numbers.

Answer 14

for instance 1 and 1 works

Answer 15

ok that means that this equation is wrong because ifor example if you put a as 4 and b as 6 it would be wrong cause 2* 4*6 it would be 48 and the second would be 16+36 or 52

Answer 16

Yes, while it works for some cases it does not work for all. You have proved by contradiction that the statement is false.

Answer 17

thanks!!

Answer 18

In general: \(a^2+b^2 =2ab\\a^2-2ab+b^2=(a-b)^2=0\\\Longleftrightarrow a=b\)
Therefore, for any \(a\neq b\) \(a^2+b^2 \neq 2ab\)