Question

The sum of 2 consecutive natural numbers and the square of first is 5329. What are the numbers ?
Give steps.​

Answer 1

Step-by-step explanation:

Let the natural number be x then the number consecutive to x will be x + 1.

It is said that the sum of two consecutive natural numbers and the square of the first is 5329.

So, according to the above equation can be formulated as:

x + (x + 1) + x2 = 5329

On solving further we get,

x2 + 2x + 1 = 5329……………..(1)

We can say x2 + 2x + 1 is nothing but (x + 1)2

So, (1) can be written as:

(x + 1)2 = 5329

Then, (x + 1) = 5329−−−−√

Square root of 5329 is nothing but 73.

So, x + 1 = 73

And x = 72

Therefore the two numbers are 72 and 73.

Answer 2

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Let the two consecutive natural numbers be a and a+1.

According to the question,

⇒ a+(a+1)+a² =5329

⇒ 2a+1+a² =5329

⇒ a² +2a+1=5329

⇒ (a+1)² =5329

⇒ a+1=73

⇒ a=72

Thus, the two numbers are 72 and 73.