Question

3. The product of two consecutive odd numbers is 10 more than the square of the smaller number. Find the smaller number.​

Answer 1

Let:

• 2 consecutive odd numbers be x and (x + 2)

In the given question,

Their product is 10 more than square of smaller number.

So,

x (x + 2) = 10 + x²

⇒ x² + 2x = 10 + x²

Cancelling x² on both sides,

2x = 10

⇒ x = 10 ÷ 2

⇒ x = 5

∴ The smaller number = 5

EXTRA INFORMATION:

Earlier x and (x + 2) were considered as 2 numbers.

Hence, other number would be (5 + 2) which is equal to 7.

Answer 2

Answer:

5 is the smaller number

Step-by-step explanation:

Let the first odd number be x

Then the second consecutive odd number will be x+2 as we need to main that it's a odd number,

Atq,

X(x+2)=10+x²

X²+2x=10+x²

X²-x²+2x=10

2x=10

X=10/2

X=5

The second number will be x+2 = 5+2 = 7

So the numbers will be 5 and 7

The smaller number here is 5

Verify:

5(7)=10+5²

35=10+25

35=35

They are equal and hence it means our answer is correct