Question

Sum of the squares of the 3 consecutive natural numbers is 677. Determine the largest number of the three.

Answer 1

Answer:

required answer is 16....

Answer 2

The largest natural number is 16.

Step-by-step explanation:

Let the three consecutive natural numbers = x, (x + 1) and (x + 2)

To find, the largest natural number = ?

According to question,

$x^{2} +(x+1)^{2} +(x+2)^{2} =677$

⇒ $x^{2} +x^{2}+2x+1 +x^{2}+4x+4 =677$

⇒ $3x^{2} +6x+5=677$

⇒ $3x^{2} +6x-672=0$

Divided by 3, we get

$x^{2} +2x-224=0$

⇒ $x^{2} +16x-14x-224=0$

⇒ x(x + 16) - 14(x + 16) = 0

⇒ (x + 16) (x - 14) = 0

⇒ x = 14 or - 16

∴ x = 14 [∵ - 16 is not a natural number]

∴ x + 1 = 14 + 1 = 15 and

x + 2 = 14 + 2 = 16

Thus, the largest natural number is 16.