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the sum of two naturals number is8and sum of their reciprocal is 8/15. find the numbers. |
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Answer» Let first no. be x and second no. 8-xAccording to question1/x + 1/8-x = 8/158/8x - x2\xa0= 8/158x - x2\xa0\u200b\u200b\u200b\u200b\u200b\u200b= 15x2\xa0- 8x + 15 = 0x2\xa0- 5x - 3x - 15 = 0x = 3, 5Therefore first no. = 3 ; second no = 5 Let One number = xThen 2nd number = 8-xAccording to question{tex}{1\\over x} + {1\\over 8-x}= {8\\over 15}{/tex}{tex}=> {8-x+x\\over x(8-x)} = {8\\over 15}{/tex}{tex}=> {8\\over x(8-x)} = {8\\over 15} {/tex}{tex}=> {1\\over 8x-x^2} = {1\\over 15} {/tex}{tex}=> 8x-x^2 = {15} {/tex}{tex}=>x^2 -8x+ {15} =0{/tex}{tex}=>x^2 -5x-3x+ {15} =0{/tex}=> x(x-5)-3(x-5)=0=> (x-5)(x-3)=0=> x = 5 or 3If first number is 3 then 2nd number is 5.If first number is 5 then 2nd number is 3. |
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