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CBSE Class 10 Answered

The sum of two numbers is 8 and sum of their reciprocal is 8/15, find the numbers.
Asked by CHIDAMBAR | 23 May, 2018, 07:02: PM
answered-by-expert Expert Answer
Let the numbers be x and y.
x + y = 8 .....(i)
begin mathsize 16px style 1 over straight x plus 1 over straight y equals 8 over 15 fraction numerator straight x plus straight y over denominator xy end fraction equals fraction numerator begin display style 8 end style over denominator begin display style 15 end style end fraction 8 over xy equals fraction numerator begin display style 8 end style over denominator begin display style 15 end style end fraction rightwards double arrow xy equals 15 rightwards double arrow straight x equals 15 over straight y Put space it space in space left parenthesis straight i right parenthesis 15 over straight y plus straight y equals 8 15 plus straight y to the power of 2 to the power of space space end exponent end exponent equals space 8 straight y straight y to the power of 2 space end exponent minus 8 straight y plus 15 equals 0 open parentheses straight y minus 5 close parentheses open parentheses straight y minus 3 close parentheses equals 0 straight y equals 5 space or space straight y equals 3 straight y equals 5 space then space straight x space equals space 3 straight y space equals space 3 space then space straight x space equals space 5 end style
Hence, numbers are 3 and 5.
Answered by Sneha shidid | 24 May, 2018, 09:13: AM

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