Question

If x, y are positive integers with 45x = y square, What is the smallest possible value of x + y.... ​

Answer 1

Given: x, y are positive integers with y² = 45x .

To find: The smallest possible value of x + y.

Solution:

• Now we have given the equation as:

                 y² = 45x

• We can write this equation as:

                 y² = 3 × 3 × 5 × x

                 y²  = 3² × 5 × x

• Now we have given that x & y are integer.

• So the smallest value of x will be 5

                 y² = 3² × 5 × 5

                 y² = 5² × 3²

                 y² = 15²

                 y = 15

• So the value of y is 15.

• Now we have x = 5 and y  = 15, so:

                 x + y = 5 + 15

                 x + y = 20

Answer:

           So the smallest possible value of x + y is 20.