Question

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

Answer 1

only if a=b

Answer 2

is it true or false?

Answer 3

is it true?

Answer 4

Sam, did you not see Steve's reply?

why not try some values?

e.g. let a = 4, b = 5
then 2ab= 2(4)(5) = 40
a^2 + b^2 = 16 + 25 = 41

so what do you think?

Answer 5

Solution for the variable b

b=a

Answer 6

[AI-generated answer — Explain Bot]

To prove that the equation 2ab = a^2 + b^2 holds for all real numbers a and b, we can use algebraic manipulation. Let's start with the equation given:

2ab = a^2 + b^2

We can rearrange this equation to isolate one of the variables on one side:

2ab - a^2 = b^2

Now, notice that the equation can be written as a quadratic equation by changing the order of terms:

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

This quadratic equation can further be factored:

(a - b)^2 = 0

From the factored form, we can conclude that the equation is true if and only if (a - b) = 0.

This means that a must equal b in order for the equation to hold for all real numbers a and b. Therefore, the original equation 2ab = a^2 + b^2 holds true if a = b.