Question

If "from the square of a half the sum of two numbers we subtract the square of a half their difference the result is the:

• A. sum of the two numbers
• B. quotient of the two numbers
• C. difference of the two numbers
• D. product of the two numbers

Answer 1

Answer: (D)

product of the two numbers

Let two number $x$ and $y$.
Now sum of these two numbers = $x+y$
Now Half of these two number = $\frac{x+y}{2}$
Now square will be = ${\left(\frac{x+y}{2}\right)}^2$
Now if we subtract x and y and than half of these numbers will be $\frac{x-y}{2}$
Square will be ${\left(\frac{x-y}{2}\right)}^2$
Now subtracting
$\Rightarrow {\left(\frac{x+y}{2}\right)}^2-{\left(\frac{x-y}{2}\right)}^2$
$\Rightarrow \frac{x^2+2xy+y^2}{4}-\frac{x^2-2xy+y^2}{4}$
$\Rightarrow \frac{x^2+2xy+y^2-x^2+2xy-y^2}{4}$
$\Rightarrow \frac{4xy}{4}=xy$
Hence it will be the product of the two numbers