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Misc 8 - Solve 27x2 - 10x + 1 = 0 - Class 11 CBSE NCERT - Miscellaneous

  1. Chapter 5 Class 11 Complex Numbers
  2. Serial order wise
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Misc 8 Solve the equation 27๐‘ฅ2 โ€“ 10๐‘ฅ + 1 = 0 27๐‘ฅ2 โ€“ 10๐‘ฅ + 1 = 0 The above equation is of the form ๐‘Ž๐‘ฅ2 + ๐‘๐‘ฅ + ๐‘ = 0 Where a = 27, b = โ€“10, and c = 1 ๐‘ฅ = (โˆ’๐‘ ยฑ โˆš( ๐‘^2 โˆ’ 4๐‘Ž๐‘ ))/2๐‘Ž = (โˆ’ ( โˆ’ 10 ) ยฑ โˆš(( โˆ’ 10 )^2 โˆ’ 4 ร— ( 27 ) ร— ( 1 )))/(2 ร— 27) = (10 ยฑ โˆš(100 โˆ’ 108))/(2 ร— 27) = (10 ยฑ โˆš(โˆ’8))/(2 ร— 27) = (10 ยฑ โˆš(โˆ’2 ร—4 ))/(2 ร— 27) = (10 ยฑ 2โˆš(โˆ’ 2))/(2 ร— 27) = (2 (5 ยฑ โˆš(โˆ’2)))/(2 ร— 27) = (5 ยฑ โˆš(โˆ’2))/27 = (5 ยฑ โˆš(2 ร—โˆ’1))/27 = (5 ยฑ โˆš2 ร—โˆš(โˆ’1))/27 = (5 ยฑ ๐‘–โˆš2 )/27 Thus, ๐‘ฅ = (5 ยฑ ๐‘–โˆš2 )/27

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