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Example 14 - Find roots (i) x + 1/x = 3 (ii) 1/x - Examples

  1. Chapter 4 Class 10 Quadratic Equations
  2. Serial order wise
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Example 14 Find the roots of the following equations: (i) x + 1/๐‘ฅ=3,๐‘ฅโ‰ 0 x + 1/๐‘ฅ=3 (๐‘ฅ (๐‘ฅ) + 1)/๐‘ฅ=3 (๐‘ฅ2 + 1)/๐‘ฅ=3 x2 + 1 = 3x x2 โ€“ 3x + 1 = 0 We will factorize by quadratic formula Comparing equation with ax2 + bx + c = 0 Here, a = 1, b = โ€“3, c = 1 We know that D = b2 โ€“ 4ac D = (โ€“3)2 โ€“ 4 (1) (1) D = 9 โ€“ 4 D = 5 So, the roots of the equation is given by x = (โˆ’ ๐‘ ยฑ โˆš๐ท)/2๐‘Ž Putting values x = (โˆ’ (โˆ’3) ยฑ โˆš5)/(2 ร— 1) x = (3 ยฑ โˆš5)/2 Hence, the roots of the equation are (3 + โˆš5)/2 & (3 โˆ’ โˆš5)/2 , Example 14 Find the roots of the following equations: (ii) 1/๐‘ฅโˆ’1/(๐‘ฅโˆ’2)=3,๐‘ฅโ‰ 0,2 1/๐‘ฅโˆ’1/(๐‘ฅ โˆ’ 2)=3 ((๐‘ฅ โˆ’ 2) โˆ’ ๐‘ฅ )/(๐‘ฅ(๐‘ฅ โˆ’ 2))=3 (โˆ’2 )/(๐‘ฅ(๐‘ฅ โˆ’ 2))=3 โ€“2 = 3x(x โ€“ 2) โ€“2 = 3x2 โ€“ 6x 0 = 3x2 โ€“ 6x + 2 3x2 โ€“ 6x + 2 = 0 We solve this equation by quadratic formula 3x2 โ€“ 6x + 2 = 0 Comparing equation with ax2 + bx + c = 0 Here, a = 3, b = โ€“6, c = 2 We know that D = b2 โ€“ 4ac D = (โ€“ 6)2 โ€“ 4ร—(3)ร—(2) D = 36 โ€“ 24 D = 12 So, the roots of the equation is given by x = (โˆ’ ๐‘ ยฑ โˆš๐ท)/2๐‘Ž Putting values x = (โˆ’(โˆ’ 6) ยฑ โˆš12)/(2 ร— 3) x = (6 ยฑ โˆš12)/6 x = (6 ยฑ โˆš(4 ร— 3))/6 x = (6 ยฑ โˆš(4 ) ร—โˆš3)/6 x = (6 ยฑ 2 โˆš3)/6 x = (2(3 ยฑ โˆš3))/(2 ร— 3) x = (3 ยฑ โˆš3)/3 So , the roots of the equation are (3 + โˆš3)/3 and (3 โˆ’ โˆš3)/3

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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