Chapter 4: Quadratic Equations

Example – 17. The difference of squares of two numbers is 180. The square of smaller number is 8 times the larger number. Find the two numbers.

Solution :- Let larger number be x and smaller number y.

The give condition is that, x² – y² = 180 -----  (1) and y² = 8x ----- (2).

Putting y² = 8x from (2) to (1) we get,
                                             x² – 8x = 180
Or,                               x² – 8x – 180 = 0
Or,                              (x – 18)(x + 10) = 0
Thus,                                  x = 18  or  – 10
When x = 18, y² = 8 × 18 = 144, i.e. y = ±12
Hence, x = 18, y = 12   or   x = 18, y = – 12.