Question

There are 5 consecutive odd numbers. If the difference between the square of the average of the
first two odd numbers and square of the average of the last two odd numbers is 492, what is the
smallest odd number?​

Answer 1

Given:-

•There are 5 consecutive odd numbers.

•the difference between the square of the average of the

first two odd numbers and square of the average of the last two odd numbers is 492.

To Find:-

•what is the smallest odd number?

Solution:-

Let consider five consecutive odd numbers be x-4,x-2,x+2,x+4.

According to the question,

Difference between square of the average of first two odd number and the of the average last two odd numbers is 396.i.e,x+3 and x-3.

$\: \: \sf \: {(x + 3)}^{2} - {(x - 3)}^{2} = 396 \\ \\ \: \: \sf \: {x}^{2} + 9 + 6x + {x}^{2} + 6x - 9 = 396 \\ \\ \: \: \sf \: 12x = 396 \\ \\ \: \: \sf \: x = 33$

Hence,the smallest odd number is 33-4 = 29.

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Answer 2

Step-by-step explanation:

$\bf \large \underline{Answer:}$

Given:

• There are 5 consecutive odd numbers.
• If the difference between the square of the average of the first two odd numbers and square of the average of the last two odd numbers is 492

To Find :

• what is the smallest odd number

Let us assume that,

Five odd consecutive number x , x+2 ,x+4 ,x+6 and x+8

According to question,

(x+6+x+8/2)² - (x+x+2/2)² = 492

(2x+14/2)² - (2x-2/2)² = 492

(x+7)²-(x+1)² = 492

x²+14x-49-x²-2x-1 = 492

12x + 48= 492

12 x = 492-48

12x = 444

x= 444/12

x= 37

•°• Smallest odd number is 37 !!

Proof :

The number are 37,39,41,43,45

According to question,

average of the first two odd numbers:

37+39/2=38

38²=1444

average of the last two odd numbers:

43+45/2=44

44²=1936

The difference is 1936 - 1444= 492

Thus the smallest odd number is 37 !!!

# Sanjushri Reddy

#Make it easy