Ex 5.3, 10 - Class 11 CBSE - Solve x2 + x/root 2 + 1 = 0 - Ex 5.3

  1. Chapter 5 Class 11 Complex Numbers
  2. Serial order wise
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Ex 5.3, 10 Solve the equation ๐‘ฅ2 + x/โˆš2 + 1=0 x2 + x/โˆš2 + 1 = 0 Multiply the equation by โˆš2 โˆš2 ร— (๐‘ฅ^2+๐‘ฅ/โˆš2+1) = โˆš2 ร— 0 โˆš2 x2 + โˆš2 ร— ๐‘ฅ/โˆš2 + โˆš2 ร— 1 = 0 โˆš2x2 + x + โˆš2 = 0 The above equation is of the form ๐‘Ž๐‘ฅ2 + ๐‘๐‘ฅ + ๐‘ = 0 Where a = โˆš2 , b = 1, and c = โˆš2 ๐‘ฅ = (โˆ’๐‘ ยฑ โˆš( ๐‘^2 โˆ’ 4๐‘Ž๐‘ ))/2๐‘Ž = (โˆ’1 ยฑ โˆš(1^2 โˆ’ 4 ร— โˆš(2 )ร— โˆš2) )/(2 ร— โˆš2) = (โˆ’1 ยฑ โˆš(1 โˆ’ 4 ร— 2))/(2โˆš2) = (โˆ’1ยฑ โˆš(1 โˆ’ 8))/(2โˆš2) = (โˆ’1ยฑ โˆš(โˆ’7))/(2โˆš2) = (โˆ’1ยฑ โˆš(โˆ’1ร— 7))/(2โˆš2) = (โˆ’1ยฑ โˆš7ร—โˆš(โˆ’1))/(2โˆš2) = (โˆ’1ยฑ โˆš7 ๐‘–)/(2โˆš2) Thus, ๐‘ฅ = (โˆ’1ยฑ โˆš7 ๐‘–)/(2โˆš2)

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