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

Last updated at Dec. 16, 2024 by

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

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

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If a = 5 + 2√6 and b = 1/𝑎, then what will be the value of 𝑎^2+𝑏^2 ? a = 5 + 2√6 b = 1/𝑎 = 1/(5 + 2√6) = 1/(5 + 2√6) × (5 − 2√6)/(5 − 2√6) = (5 − 2√6)/(5^2 − (2√6)^2 ) = (5 − 2√6)/(25 − 24) We know that 〖(𝑎+𝑏)〗^2 = 𝑎^2+𝑏^2+ 2𝑎𝑏 𝒂^𝟐+𝒃^𝟐 = 〖(𝒂+𝒃)〗^𝟐 − 𝟐𝒂𝒃 Here, 𝒂+𝒃 = (5+2√6)+5(5−2√6) 𝒂𝒃 = (5+2√6) (5−2√6) Thus, 𝑎^2+𝑏^2 = 〖(𝑎+𝑏)〗^2 − 2𝑎𝑏 𝑎^2+𝑏^2=〖10〗^2−2 × 1 =100−2 =𝟗𝟖

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo