Saved Bookmarks
| 1. |
Solve the quadratic equation by factorization x+1/x-1-x-1/x+1=5/6 |
| Answer» We have,{tex}\\frac{{x + 1}}{{x - 1}} - \\frac{{x - 1}}{{x + 1}} = \\frac{5}{6}{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}\\frac{(x+1)^2-(x-1)^2}{(x-1)(x+1)}= \\frac56{/tex}{tex}\\Rightarrow{/tex} (x2 + 1 + 2x) - (x2 + 1 - 2x) = {tex}\\frac{5}{6}{/tex}(x2 - 12){tex}\\Rightarrow{/tex} x2 + 1 + 2x - x2 - 1 + 2x = {tex}\\frac{5}{6}{/tex}(x2 - 1){tex}\\Rightarrow{/tex} 4x = {tex}\\frac{5}{6}{/tex}(x2 - 1){tex}\\Rightarrow{/tex} 24x = 5(x2 - 1){tex}\\Rightarrow{/tex}\xa024x = 5x2 - 5{tex}\\Rightarrow{/tex}\xa05x2 - 24x - 5 = 0{tex}\\Rightarrow{/tex} 5x2 - 25x + 1x - 5 = 0{tex}\\Rightarrow{/tex} 5x(x - 5) + 1(x - 5) = 0{tex}\\Rightarrow{/tex} (x - 5)(5x + 1) = 0{tex}\\Rightarrow{/tex} x - 5 = 0 or 5x + 1 = 0{tex}\\Rightarrow{/tex} x = 5 or {tex}x = - \\frac { 1 } { 5 }{/tex} | |