Question

Please Help!!

Complete the conjecture based on the pattern you observe in the examples below

1) Conjecture: The sum of any two odd numbers is…
1+1=2
1+5=6
7+9=16
9+11=20
13+21=34
101+103=204

2) Conjecture: The product of any two odd numbers is…
1*1=1
1*5=6
7*9=16
9*11=20
13*21=34
101*103=204

3) Conjecture: The product of a number (x-1) and the number (x+1) is always equal to…
3*5=4^2-1
4*6=5^2-1
5*7=6^2-1
7*9=8^2-1
8*10=9^2-1

Answer 1

Hello,

Explanation:

1) Conjecture: The sum of any two odd numbers is even
(2a+1)+(2b+1)=2a+2b+2=2(a+b+1) is even

2) Conjecture: The product of any two odd numbers is ODD
(2a+1)*(2b+1)=4ab+2b+2a+1=2(2ab+a+b)+1 is ODD
1*1=1

1*5=5

7*9=63

9*11=99

13*21=273

3) Conjecture: The product of a number (x-1) and the number (x+1) is always equal to the difference of the square of x between 1

(x-1)(x+1)=x²-x+x-1=x²-1