Question

A+B=25 A-B=13 find A*B=

Answer 1

so the answer is 114.....

thanksss

Answer 2

We can find it without finding the values of 'a' and 'b'!!!

Using the identity given below...

$\LARGE (a+b)^2-(a-b)^2=4ab$

Proof of identity:

$\Longrightarrow\ (a+b)^2=a^2+b^2+2ab \\ \\ \Longrightarrow\ (a-b)^2=a^2+b^2-2ab \\ \\ \\ \Longrightarrow\ (a+b)^2-(a-b)^2 \\ \\ \Longrightarrow\ (a^2+b^2+2ab)-(a^2+b^2-2ab) \\ \\ \Longrightarrow\ a^2+b^2+2ab-a^2-b^2+2ab \\ \\ \Longrightarrow\ 4ab$

Answer with explanation:

Given that,

$\rightarrow\ A+B=25 \\ \\ \rightarrow\ A-B=13 \\ \\ \\ \Rightarrow\ (A+B)^2=25^2=625 \\ \\ \Rightarrow\ (A-B)^2=13^2=169 \\ \\ \\ \\ \\ \Longrightarrow\ (A+B)^2-(A-B)^2=625-169 \\ \\ \\ \Longrightarrow\ 4AB=456 \\ \\ \\ \Longrightarrow\ AB=\displaystyle \frac{456}{4} \\ \\ \\ \Longrightarrow\ AB=\Large \textbf{114}$

Thus, the answer is 114.