Question

Two natural numbers. differ by 2. The
Sum of their Squares
is 452. Find the
numbers​

Answer 1

Answer:

14 and 16

Step-by-step explanation:

Let the numbers be x and x+2

According to question,

x² + (x+2)² = 452

=> 2x² + 4x + 4 - 452 = 0

=> x² + 2x -224 = 0

=> x² + 16x - 14x - 224 = 0

=> x(x+16)-14(x+16) = 0

=> x = 14

x+2 = 16

Answer 2

Let one of the number be = (x)

∴ Second one = (x + 2)

Sum of their squares = 452

As per condition,

(x)² + (x + 2)² = 452

⇒ x² + (x² + 4x + 4) = 452

⇒ 2x² + 4x + 4 = 452

⇒ x² + 2x + 2 = 226

⇒ x² + 2x + 2 = 226

⇒ x² + 2x + 2 - 1 = 226 - 1

{adjust LHS such that we can factor it}

⇒ x² + 2x + 1 = 225

⇒ (x + 1)² = (15)²

{factor it using (a + b)² = a² + 2ab + b²}

⇒ x + 1 = 15

⇒ x = 14.

∴ The numbers are (x) = 14 and (x + 2) = 16.