Question

The sum of the squares of two consecutive positive even numbers is 340. Find the numbers.

Answer 1

SOLUTION :

Given : Sum of the squares of positive even integers  = 340

Let x and (x + 2) be the  two positive consecutive even integers.

A.T Q

x² + (x + 2)² = 340

x² + x² + 4x + 4 - 340 = 0

[(a + b)² = a² + b² + 2ab ]

2x² + 4x - 336 = 0

2(x² + 2x - 168) = 0

x² + 2x - 168 = 0

x²  + 14x - 12x - 168 = 0

[By middle term splitting method]

x(x + 14) - 12(x + 14) = 0

(x + 14)(x - 12) = 0

(x + 14) = 0 or (x - 12) = 0

x = - 14 or x = 12

Since, x is a positive number, so x ≠ - 14. Therefore x = 12

First integer = x = 12

Second integer = (x + 2) = 12 + 2 = 14  

Hence, the two positive consecutive even integers are 12 & 14 .

HOPE THIS  ANSWER WILL HELP YOU…..

Answer 2

Answer :-

Let the two consecutive positive even integers be x+x2

given,

x sq.+x sq.+4x +4= 340

2x sq.+4x+4 - 340 = 0

2x sq.+4x - 336 = 0

by 2

x sq.+ 2x - 168 = 0

splitting the middle term

x sq.+ 14 x - 12x - 168

x (x+4) - 12 (x+4)

(x+14) (x- 12)

x = 12

Hence,
the numbers are

x = 12

x+2 = 12+2 = 14


12 and 14..