Q66 of 82 Page 4

The sum of the squares of two consecutive multiples of 7 is 637. Find the multiples. (CBSE 2014)

Let the consecutive multiples of 7 be ‘a’ and a + 7


⇒ a2 + (a + 7)2 = 637


⇒ 2a2 + 14a – 588 = 0


⇒ 2a2 + 42a – 28a – 588 = 0


⇒ 2a(a + 21) – 28(a + 21) = 0


⇒ (2a – 28)(a + 21) = 0


Thus, a = 14


Consecutive multiples of 7 are 14, 21

More from this chapter

All 82 →
64

The difference of two natural numbers is 3 and the difference of their reciprocals is . Find the numbers. (CBSE 2014)

 65

The sum of the squares of two consecutive odd numbers is 394. Find the numbers. (CBSE 2014)

 67

The sum of the squares of two consecutive even numbers is 340. Find the numbers. (CBSE 2014)

 68

The numerator of a fraction is 3 less than the denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and the original fraction is , find the original fraction. (CBSE 2015)