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.

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Subjects Maths (Part-1) by Mr. M. P. Keshari
Chapter 1 Linear Equations in Two Variables
Chapter 2 HCF and LCM
Chapter 3 Rational Expression
Chapter 4 Quadratic Equations
Chapter 5 Arithmetic Progressions
Chapter 6 Instalments
Chapter 7 Income Tax
Chapter 8 Similar Triangles