Q35 of 40 Page 1

Find two consecutive positive integers sum of whose squares is 365.

Let the two consecutive integers be x and x + 1,


⇒ x2 + (x + 1)2 = 365


⇒ x2 + x2 + 2x + 1 = 365


⇒ 2x2 + 2x – 364 = 0


⇒ x2 + x – 182 = 0




⇒ x = 13, -14


But x should be positive. So, x = 13


The consecutive integers are 13 and 14.


More from this chapter

All 40 →
33

Read the following passage and answer the questions that follows:

In a classroom, four students, Sita, Gita, Rita and Anita are sitting at A(3, 4), B(6, 7), C(9, 4), D(6, 1) respectively. Then a new student Anjali joins the class



(i) Teacher tells Anjali to sit in the middle of the four students. Find the coordinates of the position where she can sit.


(ii) Calculate the distance between Sita and Anita.


(iii) Which two students are equidistant from Gita.


 34

Solve 2x + 3y = 11 and x – 2y = -12 algebraically and hence find the value of ‘m’ for which y = mx + 3.

 36

If the sum of first 14 terms of an A.P. is 1050 and its first term is 10, find the 20th term.

OR


The first term of an A.P. is 5, the last term is 45 and sum is 400. Find the number of terms and common difference.


 37

As observed from the top of a 75m high light house above the sea level, the angles of depression of two ships are 30° and 45° respectively. If one ship is exactly behind the other on the same side of the light house and in the same straight line, find the distance between the two ships. (use √3 = 1.732)