Question

Two consecutive positive even numbers are such that the sum of their squares is 164. Find
the two numbers.​

Answer 1

Given:-

• Two consecutive positive even numbers are such that the sum of their squares is 164.

⠀

To find:-

• The two numbers.

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Solution:-

Here,

• Sum of their squares = 164

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Let,

• the first number be x.
• the second number be x + 2.

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According to the question

⇛ x² + (x+2)² = 164

⇛ 2x² + 4x + 4 = 164

⇛ x² + 2x - 80 = 0

⇛ (x - 8) × (x + 10) = 0

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Therefore,

→ First number = x = 8

→ second number = x + 2 = 8 + 2 = 10

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Hence,

• the first number is 8 and the second number is 10.

Answer 2

Given :

Two consecutive positive even numbers are such that the sum of their squares is 164.

To find :

Find  the two numbers.​

Solution :

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

So atq,

⇒ x² + (x + 2)² = 164

⇒ x² + x² + 4x + 4 = 164

⇒ 2x² + 4x + 4 - 164 = 0

⇒ 2x² + 4x - 160 = 0

⇒ 2(x² + 2x - 80) = 0

⇒ x² + 2x - 80 = 0

⇒ x² + 10x - 8x - 80 = 0

⇒ x(x + 10) - 8(x + 10) = 0

⇒ (x - 8)(x + 10) = 0

⇒ x = 8   or,   x = - 10

∵ We will neglect negative number as the numbers are positive even numbers.

∴ x = 8

∴ First number = x = 8

∴ Second number = x + 2 = 8 + 2 = 10

∴ Two consecutive positive even numbers are 8 and 10 respectively.