kmullis6
  • kmullis6
Please help, I'll give fan & medal
Mathematics
jamiebookeater
  • jamiebookeater
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kmullis6
  • kmullis6
Directions: Complete the conjecture based on the pattern you observe in the specific cases. Conjecture: The product of a number (n - 1) and the number (n +1) is always equal to _____. \[3\times5=4^{2}-1\] \[4\times6=5^{2}-1\] \[5\times7=5^{2}-1\] \[6\times8=7^{2}-1\] \[7\times9=8^{2}-1\] \[8\times10=9^{2}-1\]
misty1212
  • misty1212
HI!!
misty1212
  • misty1212
it is not clear? what do you think \[9\times 11\]would equal in that pattern?

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kmullis6
  • kmullis6
99 so odd number. that's the types of questions i'm answering right now.
misty1212
  • misty1212
lets look more carefully
misty1212
  • misty1212
the right hand side of each equal sign is some number squared minus 1 right?
kmullis6
  • kmullis6
Yes
misty1212
  • misty1212
and that number, the number being squared, is half way between the other two numbers right?
misty1212
  • misty1212
the number in the middle of \(n-1\) and \(n+1\) is just \(n\)
misty1212
  • misty1212
so what they are showing you, by example instead of by algebra, is that \[(n-1)(n+1)=n^2-1\]
kmullis6
  • kmullis6
so the answer is n?
misty1212
  • misty1212
lol no, the answer is \(n^2-1\)
kmullis6
  • kmullis6
oohhhh ok. sorry haha :P thank you (:

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