The sum of square and product of two number are 557 & 266 respectively

The sum of square and product of two number are 557 & 266 respectively. The numbers will be-
(a) 7,6
(b) 27, 23
(c) 17, 14
(d) 19, 14

Anurag Mishra Professor Asked on 8th March 2016 in Maths.
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1 Answer(s)

Answer: (d) 19, 14

Solution:-
Let the two number be X and Y.

The sum of square and product of two numbers are 557 & 266
Then, X² + Y² = 557  & X Y = 266

Now, (X + Y)² = X² + Y² + 2 x X Y
= 557 + 2 x 266
(X + Y)² = 1089
Square root on both side,
X + Y = 33 ………….. (1)

(X – Y)² = X² + Y² – 2 x X Y
= 557 – 532
(X – Y)² = 25
Square root on both side,
X – Y = 5 ……………. (2)

Add equation (1) & (2),
X + Y + X – Y = 33 + 5
2 X = 38
X = 38/2
X = 19
Put the value of X = 19 in equation (1),
Then, 19 + Y = 33
Y = 33 – 19
Y = 14

Then, two numbers are 19, 14.

Hence, the correct answer is option (d) 19, 14.

Anurag Mishra Professor Answered on 8th March 2016.
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