Q1 of 27 Page 84

1 Added to the product of two consecutive even numbers gives 289. What are the numbers?

Let the number be 2x. Therefore, the consecutive even number will be (2x + 2).


Now the product of these two numbers will be 2×(2x + 2)


Therefore, 1 added to the product will be x(x + 2) + 1 which is equal to 289


⇒ 2x (2x + 2) + 1 = 289


⇒ 4x2 + 4x + 1 = 289


⇒ (2x + 1)2 = 172


⇒ √((2x + 1)2) = √(172)


⇒ (2x + 1) = 17


⇒ 2x = 17 – 1



⇒ x = 8


One number is 16 and the other number 18


More from this chapter

All 27 →
3

The square of a term in the arithmetic sequence 2, 5, 8, …, is 2500. What is its position?

 4

2000 rupees was deposited in a scheme in which interest is compounded annually. After two years the amount in the account was 2200 rupees. What is the rate of interest?

 2

9 added to the product of two consecutive multiples of 6 gives 729. What are the numbers?

 3

An isosceles triangle has to be made like this


The height should be 2 metres less than the base. What should be the length of its sides?