Question

If the product of two numbers is $10$ and the sum is $7,$ then the larger of the two numbers is:

• A. $-2$
• B. $2$
• C. $5$
• D. $4\frac{1}{4}$

Answer 1

The correct option is C $5$

Let the smallest number be $b$ and larger be $a$

$\therefore a+b=7$ ......(i)

and $ab=10$ ....(ii)

Now, $(a-b{)}^2=(a+b{)}^2-4ab$

$=7^2-4\left(10\right)$

$=49-40$

$=9$

Therefore, $a-b=3$ ....(iii)

Solving (i) and (iii), we get

$a=5,b=2$

Hence, larger number is $5$.