Question 2 - Think and Reflect (Page 71) - Visualising Algebraic Identities - Chapter 4 Class 9 - Exploring Algebraic Identities (Ganita Manjari I)

Transcript

Question 2 - Think and Reflect (Page 71) What can you say about 𝑎 and 𝑏 if (𝑎+𝑏)^2>𝑎^2+𝑏^2? We know that (𝒂+𝒃)^𝟐=𝒂^𝟐+𝒃^𝟐+𝟐𝒂𝒃 Putting this value in our inequality (𝑎+𝑏)^2>𝑎^2+𝑏^2 𝒂^𝟐+𝒃^𝟐+𝟐𝒂𝒃>𝑎^2+𝑏^2 Taking a2 and b2 on right side 2𝑎𝑏>𝑎^2+𝑏^2−𝑎^2−𝑏^2 𝟐𝒂𝒃>𝟎 2𝑎𝑏>0/2 𝒂𝒃>𝟎 Since product ab is greater than zero, it means that a & b have same signs So, Both numbers are positive Or both numbers are negative Example: a = 8, b = 1 Or a = –102, b = –20