Q67 of 82 Page 4

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

Let the consecutive even integers be ‘a’ and a + 2


⇒ a2 + (a + 2)2 = 340


⇒ 2a2 + 4a – 336 = 0


⇒ a2 + 2a – 168 = 0


⇒ a2 + 14a – 12a – 168 = 0


⇒ a(a + 14) – 12(a + 14) = 0


⇒ (a – 12)(a + 14) = 0


Thus, a = 12 or – 14


Consecutive even integers are 12, 14 or -14, - 12

More from this chapter

All 82 →
65

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

 66

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

 69

Solve the following for x: (CBSE 2015)