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

Given,

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

Let the numbers be x and x+2.

Their squares are x² and (x+2)² .

Therefore,

x² + (x+2)² = 340

x²  + x² + 2²+2(2)(x) = 340

2x² +4x+4 = 340

2x² + 4x + 4-340 = 0

2x² + 4x -336 = 0

x² + 2x - 168 = 0

x² + 14x -12x -168 = 0

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

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

x=12

x cannot be -14 as negative numbers cannot be classified as even or odd.

Therefore,

The numbers are 12 and 12+2 = 14.

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Updated on: 10-Oct-2022

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