For all real numbers a and b, 2a • b = a^2 + b^2
only if a=b
is it true or false?
is it true?
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?
Solution for the variable b
b=a
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.