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The sum of two numbers is 8. Determine the number if the sum of there reciprocal is 8 by 15 |
| Answer» Let the two\xa0numbers are\xa0x and 8 - x.\xa0According to question,{tex}15\\left( {\\frac{1}{x} + \\frac{1}{{8 - x}}} \\right) = 8{/tex}{tex} \\Rightarrow 15\\left( {\\frac{{8 - x + x}}{{x(8 - x)}}} \\right) = 8{/tex}{tex} \\Rightarrow {/tex}\xa0{tex}15 \\times 8=8x(8-x){/tex}{tex} \\Rightarrow 15 = \\frac{{8x}}{8}(8 - x){/tex}{tex} \\Rightarrow {/tex} 15 = x(8 - x){tex} \\Rightarrow {/tex} 15 = 8x - x2{tex} \\Rightarrow {/tex} x2 - 8x + 15 = 0Factorise the equation,{tex} \\Rightarrow {/tex} x2\xa0- 5x - 3x + 15 = 0{tex} \\Rightarrow {/tex} x(x - 5) - 3(x - 5) = 0{tex} \\Rightarrow {/tex} (x - 5)(x - 3) = 0{tex} \\Rightarrow {/tex} x = 5 or x = 3Hence, required numbers are 3 and 5. | |