Question

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

Answer 1

Step-by-step explanation:

let two even consecutive numbers = 2x+2 the two consecutive are 12 and14

Answer 2

AnswEr :-

• The numbers are 12 and 14.

Given :-

• The sum of the squares of

⠀⠀ two even numbers is 340.

To Find :-

• These numbers.

SoluTion :-

Let the required consecutive even numbers be x and x + 2.

• Square of x = x²

• Square of x + 2 = (x + 2)²

According to question :-

» x² + (x + 2)² = 340

→ 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

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» x + 14 = 0

→ x = 0 - 14

→ x = - 14

» x - 12 = 0

→ x = 0 + 12

→ x = 12 [ rejecting x = - 14 ]

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Hence, the numbers are 12 and 14.

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