Question 5 - Figure it out - Page 16, 17 - Chapter 1 Class 8 - A Square and a Cube (Ganita Prakash)

Transcript

Question 5 Which of the following is the greatest? Explain your reasoning. (i) 673 – 663 (ii) 433 – 423 (iii) 672 – 662 (iv) 432 – 422 Let’s first look at Difference between consecutive cubes and Difference between consecutive squares Difference between consecutive squares 𝒏^𝟐−(𝒏−𝟏)^𝟐=𝑛^2−[𝑛^2+1−2𝑛] =𝑛^2−𝑛^2−1+2𝑛 =𝟐𝒏−𝟏 Difference between consecutive cubes 𝒏^𝟑−(𝒏−𝟏)^𝟑=𝑛^3−[𝑛^3+1^3−3𝑛(𝑛−1) ] =𝑛^3−[𝑛^3+1−3𝑛^2+3𝑛] =𝑛^2−𝑛^3−1+3𝑛^2−3𝑛 =𝟑𝒏^𝟐−𝟑𝒏−𝟏 Thus, Difference between consecutive cubes is greater than between consecutive squares And, value of the difference increase as number increases Since n = 67 is the largest value of n Therefore, Greatest value is (i) 673 − 663