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:

  1. 3
  2. 4
  3. 5
  4. 7
Monis Rasool Professor Asked on 25th October 2015 in Maths.
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1 Answer(s)

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 = 422
X2  + Y2 + 2 X Y = 42 x 42
X2 + Y2 + 2 x 437 = 1764                             {From equation (2)}
X2 + Y2 + 874 = 1764
X2 + Y2 = 1764 – 874
X2 + Y2 = 890 …………………………… (3)

Now, (X – Y)2 = X2 + Y2= – 2 X Y
Put the value X Y = 437 and X2 + Y2 = 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.

Anurag Mishra Professor Answered on 25th October 2015.
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