# What will be the difference?

The sum of two numbers is 42 and their product is 437. Then the absolute difference between the numbers is:

- 3
- 4
- 5
- 7

**Answer: (2) 4**

**Explanation:-
**Let the two numbers are X and Y

The sum of two numbers is 42

Then, X + Y = 42 …………………………. (1)

Their product is 437,

Then, X Y = 437 ……………….. (2)

From equation (1),

X + Y = 42

Squaring on both side,

(X + Y)^{2 }= 42^{2}

X^{2 } + Y^{2} + 2 X Y = 42 x 42

X^{2} + Y^{2} + 2 x 437 = 1764 {From equation (2)}

X^{2} + Y^{2} + 874 = 1764

X^{2} + Y^{2} = 1764 – 874

X^{2} + Y^{2} = 890 …………………………… (3)

Now, (X – Y)^{2} = X^{2} + Y^{2}= – 2 X Y

Put the value X Y = 437 and X^{2} + Y^{2} = 890

Then, (X – Y)^{2} = 890 – 2 x 437

(X – Y)^{2} = 890 – 874

(X – Y)^{2} = 16

Square root on both side,

X – Y = 4

Then, the difference between the numbers is 4.

Hence, the answer is (2) 4.