Divide a given square number say 16 into the sum of two squa

Divide a given square number, say 16, into the sum of two squares. Following Diophantus\' idea, by using the modern notation, let one of the required squares be x2. Then 16 - x2 must be equal to a square. Assume that this square is (2x - 4)2 where x is the unknown. Please complete the solution.

Solution

Dividing the square number 16 into two squares, let first number be x^2 and second number be (16-x^2)

Now equating the equations we get

(2x-4)^2 = 16-x^2

4x^2 + 16 - 16x = 16 - x^2

5x^2 = 16x

Hence we get x = 16/5

so one number will be 16/5

another number will be

second^2 = 16 - 256/25 = 144/25 = 12/5

Hence the numbers are 16/5 and 12/5