Question

If the product of two number is 48 and sum of square of the number is 100.Then what will be the sum of the number?

Answer 1

Let the two numbers be x and y

According to question,

x*y = 48....(1)

=> x = 48/y....(2)

x^2 + y^2 = 100....(3)

We know, (a+b)^2 = a^2 + b^2 +2ab

=>a^2 + b^2 = (a+b)^2 - 2ab

We can write (3) as,

(x+y)^2 - 2xy = 100

From (1),

(x+y)^2 - 2*48 = 100

(x+y)^2 - 96 = 100

(x+y)^2 = 100 + 96

(x+y)^2 = 196

(x+y) = 14

From (2),

48/y + y = 14

Multiplying throughout by y

48 + y^2 = 14y

y^2 - 14y + 48 = 0

y^2 - 8y - 6y + 48 = 0

y(y - 8) - 6(y - 8) = 0

(y - 8)(y - 6) = 0

=> y - 8 = 0

y = 8

y - 6 = 0

y = 6

From (2),

x = 48/y

=> x = 48/8

x = 6

x = 48/6

x = 8

Therefore the numbers are 8 and 6.