Question

the product of two consecutive odd numbers is 899.find the numbers

Answer 1

Answer:

899 is just 1 less than 900. And 900 is the square of 30. And 1 is the square of 1. So 899 is the difference of two squares.

Explanation:

We have a special product here, of the form:
(A−B)(A+B)=A2−B2

If we take 30and1 for AandB:
(30−1)(30+1)=302−12=900−1=899BINGO!

So the answer is 29and31

Note : of course −29and−31 also count as a solution.

Answer 2

Answer:

Two numbers are 2×14+1= 29 and 2×14+3 = 31

or 2×(-16)+1= -31 and 2×(-16)+3 = -29

Explanation:

Let two numbers be 2n+1 and 2n+3

According to question,

(2n+1) ×(2n+3) = 899

4n^2+6n+2n+3 = 899

4n^2 +8n+3 = 899

4n^2 + 8n +3 - 899 =0

4n^2 + 8n -896 = 0

4(n^2 + 2n - 224) = 0

n^2 + 2n - 224 = 0

solve this equation by middle term,

n = 14 or -16

Two numbers are 2×14+1= 29 and 2×14+3 = 31

or 2×(-16)+1= -31 and 2×(-16)+3 = -29