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| 1. |
Find the roots.(x-5)(x-6)=25/24² |
| Answer» According to the question,{tex}(x - 5)(x - 6) = \\frac{{25}}{{{{\\left( {24} \\right)}^2}}}{/tex}{tex}\\Rightarrow x(x - 6) - 5(x - 6) = \\frac{{25}}{{{{(24)}^2}}}{/tex}{tex}\\Rightarrow {x^2} - 6x - 5x + 30 - \\frac{{25}}{{{{(24)}^2}}} = 0{/tex}{tex}\\Rightarrow {x^2} - 11x + 30 - \\frac{{25}}{{{{(24)}^2}}} = 0{/tex}{tex}\\Rightarrow {x^2} - 11x + \\frac{{30 \\times {{24}^2} - 25}}{{{{(24)}^2}}} = 0{/tex}{tex} \\Rightarrow {x^2} - 11x + \\frac{{30 \\times 576 - 25}}{{{{(24)}^2}}} = 0{/tex}{tex} \\Rightarrow {x^2} - 11x + \\frac{{17280 - 25}}{{{{(24)}^2}}} = 0{/tex}{tex}\\Rightarrow {x^2} - \\frac{{264x}}{{24}} + \\frac{{145}}{{24}} \\times \\frac{{119}}{{24}} = 0{/tex}{tex}\\Rightarrow {x^2} - \\left( {\\frac{{145}}{{24}} + \\frac{{119}}{{24}}} \\right)x + \\frac{{145}}{{24}} \\times \\frac{{119}}{{24}} = 0{/tex}{tex}\\Rightarrow {x^2} - \\frac{{145}}{{24}}x - \\frac{{119}}{{24}}x + \\frac{{145}}{{24}} \\times \\frac{{119}}{{24}} = 0{/tex}{tex}\\Rightarrow x\\left( {x - \\frac{{145}}{{24}}} \\right) - \\frac{{119}}{{24}}\\left( {x - \\frac{{145}}{{24}}} \\right) = 0{/tex}{tex}\\Rightarrow \\left( {x - \\frac{{145}}{{24}}} \\right)\\left( {x - \\frac{{119}}{{24}}} \\right) = 0{/tex}{tex}\\Rightarrow x - \\frac{{145}}{{24}} = 0{/tex} or {tex}x - \\frac{{119}}{{24}} = 0{/tex}{tex}\\Rightarrow x = \\frac{{145}}{{24}}{/tex} or {tex}x = \\frac{{119}}{{24}}{/tex} | |