Question 1 - Think and Reflect (Page 71) - Visualising Algebraic Identities - Chapter 4 Class 9 - Exploring Algebraic Identities (Ganita Manjari I)

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Question 1 - 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 less than zero, it means that a & b have opposite signs So, one number has to be negative, other has to be positive Example: a = 5, b = –3 Or a = –2, b = 100