Question 7 - Figure it out - Page 154-156 - Chapter 6 Class 8 - We Distribute yet things Multiply (Ganita Prakash)

Transcript

Question 7 Choose three consecutive numbers, square the middle one, and subtract the product of the other two. Repeat the same with other sets of numbers. What pattern do you notice? How do we write this as an algebraic equation? Expand both sides of the equation to check that it is a true identity.Three consecutive numbers are 𝑛, 𝑛+1, 𝑛+2 Now, we have to square the middle one, and subtract the product of the other two. We get (𝒏+𝟏)^𝟐−𝒏(𝒏+𝟐) = 𝑛^2+2𝑛+1−[𝑛^2+2𝑛] = 𝑛^2+2𝑛+1−𝑛^2−2𝑛 = 1 Thus, no matter what number we choose, the result is 1