If a = 5 + 2√6 and b = 1/a, then what will be the value of a^2+b^2 ?

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If a = 5 + 2√6 and b = 1/a, then what will be the value of a^2+b^2 ? - Part 2

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If a = 5 + 2√6 and b = 1/a, then what will be the value of a^2+b^2 ? - Part 3

  1. Chapter 1 Class 9 Number Systems (Term 1)
  2. Concept wise

Transcript

If a = 5 + 2โˆš6 and b = 1/๐‘Ž, then what will be the value of ๐‘Ž^2+๐‘^2 ? a = 5 + 2โˆš6 b = 1/๐‘Ž = 1/(5 + 2โˆš6) = 1/(5 + 2โˆš6) ร— (5 โˆ’ 2โˆš6)/(5 โˆ’ 2โˆš6) = (5 โˆ’ 2โˆš6)/(5^2 โˆ’ (2โˆš6)^2 ) = (5 โˆ’ 2โˆš6)/(25 โˆ’ 24) We know that ใ€–(๐‘Ž+๐‘)ใ€—^2 = ๐‘Ž^2+๐‘^2+ 2๐‘Ž๐‘ ๐’‚^๐Ÿ+๐’ƒ^๐Ÿ = ใ€–(๐’‚+๐’ƒ)ใ€—^๐Ÿ โˆ’ ๐Ÿ๐’‚๐’ƒ Here, ๐’‚+๐’ƒ = (5+2โˆš6)+5(5โˆ’2โˆš6) ๐’‚๐’ƒ = (5+2โˆš6) (5โˆ’2โˆš6) Thus, ๐‘Ž^2+๐‘^2 = ใ€–(๐‘Ž+๐‘)ใ€—^2 โˆ’ 2๐‘Ž๐‘ ๐‘Ž^2+๐‘^2=ใ€–10ใ€—^2โˆ’2 ร— 1 =100โˆ’2 =๐Ÿ—๐Ÿ–

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.