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The sum of two numbers is 9 and the sum of their reciprocals is 1÷2. Find the numbers |
| Answer» Let one number be x.Then, another number = (9 - x) [{tex}\\because{/tex} sum of two numbers = 9]According to the question,{tex}\\begin{array}{l}\\frac1x+\\;\\frac1{9-x}=\\;\\frac12\\\\\\frac{9\\;-x+x}{x(9-x)}\\;=\\frac12\\end{array}{/tex}\xa0⇒ 18 = 9x - x2{tex}\\Rightarrow {x^2} - 9x + 18 = 0 {/tex}{tex}\\Rightarrow {x^2} - 6x - 3x + 18 = 0{/tex}{tex}\\Rightarrow x=3,x=6{/tex}When, x = 3, then 9 - x = 9 - 3 = 6When, x = 6, then 9 - x = 9 - 6 = 3Hence, the numbers are 3 and 6. | |