Question
The product of 2 numbers is 120. Sum of their square is 289. What is the sum of these 2 numbers ??
Answer
Let the two numbers be x and y.
According to data, x * y = 120
And x^2 + y^2 = 289
By looking at given equations, we can conclude
( x + y )^ 2 = x ^ 2 + y ^ 2 + 2xy
Here we know x * y = 120
x ^ 2 + y ^2 = 289
Thus the above equation becomes,
( x + y ) ^ 2 = x ^2 + y ^ 2 + 2xy
==>> ( x + y ) ^ 2 = 289 + 2 * 120
==>> ( x + y ) ^ 2 = 289 + 240
==>> ( x + y ) ^ 2 = 529
Taking sqrt on both the sides,
==>> ( x + y ) = sqrt 529
==>> ( x + y ) = 239
Now we have x+ y = 23 and xy = 120
Checking different values of x and y resulting in sum of 23 and product of 120
We figure out,
8 * 15 = 120
8 + 15 = 23
The numbers are 8 and 15 !!!