Q2 of 227 Page 107

The difference of the squares of two positive numbers is 45. The square of the smaller number is four times the larger number. Find the numbers.

Let ‘x’ be the larger number and ‘y’ be the smaller number.


x2 – y2 = 45 …(1)


y2 = 4x …(2)


Now, put the value of y2 in equation (1).


x2 – 4x = 45


⇒ x2 – 4x – 45 = 0


⇒ x2– 9x + 5x – 45 = 0


⇒ x(x – 9) + 5(x – 9) = 0


⇒ (x + 5)(x – 9) =0


x + 5 = 0 or x – 9 = 0


x = –5 or x = 9


Here positive 9 only admissible. From this we need to find the value of y for that we are going to aplly this value in the second equation.


y2 = 4 x


⇒ y2 = 4 × 9


⇒ y2 = 36


⇒ y = √36


⇒ y = ± 6


Here, positive 6 only admissible.


Therefore, the required numbers are 6 and 9.


More from this chapter

All 227 →
2

Solve the following quadratic equations using quadratic formula.

a2x2 + (a2 – b2) x – b2 = 0

 1

The sum of a number and its reciprocal is . Find the number.

 3

A farmer wishes to start a 100 sq. rectangular vegetable garden. Since he has only 30 m barbed wire, he fences the sides of the rectangular garden letting his house compound wall act as the fourth side fence. Find the dimension of the garden.

 4

A rectangular field is 20 m long and 14 m wide. There is a path of equal width all around it having an area of 111 sq. meters. Find the width of the path on the outside.