Question

Express the square of the 9 as sum of two consecutive numbers

Answer 1

9² = 40 + 41

Given data:

The square of 9

To find:

An expression of the square of 9 as the sum of two consecutive numbers

Step-by-step explanation:

Step 1 of 2. (Finding the square of 9)

Square of a number means to find its product taken the number twice.

Here, 9² = 9 × 9 = 81

Step 2 of 2. (Finding the two numbers)

Let 9² = 81 be the sum of two consecutive numbers x and x + 1.

Then, clearly, we can write

x + (x + 1) = 81

⇒ x + x + 1 = 81

⇒ 2x + 1 = 81

⇒ 2x = 81 - 1 = 80

⇒ x = 80/2

⇒ x = 40

So, the two numbers are

x = 40

and x + 1 = 40 + 1 = 41

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