Question

write the following numbers as the difference of squares of consecutive natural numbers
21


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Answer 1

Answer:

Step-by-step explanation:

Given:

The difference of the square of two consecutive numbers is 21.

To find:

The two consecutive numbers.

Solution:

From the question, we can understand that the difference between the two numbers is 1.

And the difference between their square is 21.

We can take that the two numbers are x and x+1.

From the question,  

(x+1)²-x²=21,

By using the formula of(a+b)²=a²+b²+2ab,

Then, applying the (a+b)² formula to (x+1)²,

We can get,

x²+1²+(2×x×1)-x²=21,

x²+1²+2x-x²=21,

2x+1=21,

2x=21-1,

2x=20,

So,x=20/2=10,

And the second number is x+1=10+1

x+1=11

And the numbers are 10 and 11.

Hope it helps.

Answer 2

Answer:

10 and 11

Step-by-step explanation:

11 square = 121

10 square = 100

11 square - 10 square

121 - 100 = 21

(n+1)whole square - n square = n+1+n