# 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

**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.