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InterviewSolution
| 1. |
Find the roots of the equation 5x-6x-2=0 by the method of completing the square |
| Answer» 5x2 - 6x - 2 = 0Multiplying the above equation by 1/5{tex} \\Rightarrow {x^2} - \\frac{6}{5}x - \\frac{2}{5} = 0{/tex}{tex}\\Rightarrow x ^ { 2 } - \\frac { 6 } { 5 } x + \\left( \\frac { 3 } { 5 } \\right) ^ { 2 } - \\left( \\frac { 3 } { 5 } \\right) ^ { 2 } - \\frac { 2 } { 5 } = 0{/tex}{tex}\\Rightarrow \\left( x - \\frac { 3 } { 5 } \\right) ^ { 2 } = \\frac { 9 } { 25 } + \\frac { 2 } { 5 }{/tex}{tex}\\Rightarrow \\left( x - \\frac { 3 } { 5 } \\right) ^ { 2 } = \\frac { 9 + 10 } { 25 }{/tex}{tex}\\Rightarrow \\left( x - \\frac { 3 } { 5 } \\right) ^ { 2 } = \\frac { 19 } { 25 }{/tex}{tex}\\Rightarrow x - \\frac { 3 } { 5 } = \\pm \\frac { \\sqrt { 19 } } { 5 }{/tex}{tex}\\Rightarrow x = \\frac { 3 } { 5 } \\pm \\frac { \\sqrt { 19 } } { 5 }{/tex}{tex}\\Rightarrow x = \\frac { 3 + \\sqrt { 19 } } { 5 } \\text { or } x = \\frac { 3 - \\sqrt { 19 } } { 5 }{/tex} | |