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Sum of 2 no. Is 15.sum of their reciprocal is 3/10 find the no. |
| Answer» Let the numbers be x and 15 - x.According to question,{tex}\\frac { 1 } { x } + \\frac { 1 } { 15 - x } = \\frac { 3 } { 10 }{/tex}{tex}\\Rightarrow \\quad \\frac { 15 - x + x } { x ( 15 - x ) } = \\frac { 3 } { 10 }{/tex}{tex}\\Rightarrow \\quad \\frac { 15 } { x ( 15 - x ) } = \\frac { 3 } { 10 }{/tex}Cross multiply,{tex}\\Rightarrow{/tex}{tex}150=3x(15-x){/tex}{tex}\\Rightarrow{/tex}{tex}150=45x-3x^2{/tex}{tex}\\Rightarrow 150=3(15x-x^2){/tex}{tex}\\Rightarrow{/tex} x2 - 15x + 50 = 0{tex}\\Rightarrow{/tex} x2 - 10x - 5x + 50 = 0{tex}\\Rightarrow{/tex} x(x - 10) - 5(x -10) = 0{tex}\\Rightarrow{/tex} (x - 10)(x - 5) = 0{tex}\\Rightarrow{/tex} x - 10 = 0 or, x - 5 = 0 {tex}\\Rightarrow{/tex} x = 10 or, x = 5Therefore, numbers are 10 and 5 | |