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Ex 4.3, 3 - Find roots of (i) x - 1/x = 3 (ii) 1/x+4 - 1/x-7 - Ex 4.3

  1. Chapter 4 Class 10 Quadratic Equations
  2. Serial order wise
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Ex 4.3 ,3 Find the roots of the following equations: (i) x โ€“ 1/๐‘ฅ=3,๐‘ฅโ‰ 0 x โ€“ 1/๐‘ฅ=3 (๐‘ฅ(๐‘ฅ) โˆ’ 1 )/๐‘ฅ = 3 (๐‘ฅ^2 โˆ’ 1 )/๐‘ฅ = 3 x2 โ€“ 1 = 3x x2 โ€“ 3x โ€“ 1 = 0 Comparing equation with ax2 + bx + c = 0 So, a = 1, b = โ€“3, c = โ€“1 We know that D = b2 โ€“ 4ac D = ( โ€“3)2 โ€“ 4ร—1ร—โˆ’1 D = 9 + 4 D = 13 Hence, roots to equation are given by x = (โˆ’ ๐‘ ยฑ โˆš๐ท)/2๐‘Ž Putting values x = (โˆ’ (โˆ’ 3) ยฑ โˆš13)/(2 ร— 1) x = (3 ยฑ โˆš13)/2 Hence, roots to equation are x = (3 + โˆš13)/2 or x = (3 โˆ’ โˆš13)/2 Ex 4.3 ,3 Find the roots of the following equations: (ii) 1/(๐‘ฅ + 4)โˆ’1/(๐‘ฅ โˆ’ 7)=11/30,๐‘ฅโ‰ โˆ’4, 7 1/(๐‘ฅ + 4)โˆ’1/(๐‘ฅ โˆ’ 7)=11/30 ((๐‘ฅ โˆ’ 7) โˆ’ (๐‘ฅ + 4))/((๐‘ฅ + 4)(๐‘ฅ โˆ’ 7)) = 11/30 (๐‘ฅ โˆ’ 7 โˆ’ ๐‘ฅ โˆ’ 4)/((๐‘ฅ + 4)(๐‘ฅ โˆ’ 7)) = 11/30 (โˆ’11)/((๐‘ฅ + 4)(๐‘ฅ โˆ’ 7))=11/30 โˆ’(11 ร— 30)/11=(๐‘ฅ+4)(๐‘ฅโˆ’7) โ€“30 = (x + 4) (x โ€“ 7) (x + 4) (x โ€“ 7) = โ€“30 x (x โ€“ 7) + 4 (x โ€“ 7) = โ€“30 x2 โ€“ 7x + 4x โ€“ 28 = โ€“30 x2 โ€“ 3x โ€“ 28 = โ€“30 x2 โ€“ 3x โ€“ 28 + 30 = 0 x2 โ€“ 3x + 2 = 0 Factorizing by quadratic method Comparing with ax2 + bx + c = 0 Here a = 1, b = โ€“ 3, c = 2 We know that D = b2 โ€“ 4ac D = ( โ€“ 3)2 โ€“ 4ร—1ร—2 D = 9 โ€“ 8 D = 1 Hence roots to equation are x = (โˆ’ ๐‘ ยฑ โˆš๐ท)/2๐‘Ž Putting the values x = (โˆ’ (โˆ’ 3) ยฑ โˆš1)/(2 ร— 1) x =(3 ยฑ 1)/2 Solving Hence x = 2 and x = 1 are the roots of the equation

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