Question

If the sum of two no. is 8 and sum of their reciprocals is 8/15 then find the numbers no. .
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Answer 1

Answer:

the numbers are 5 and 3

Step-by-step explanation:

1) fund out the options ( in this case - 7+1 or 6+2 or 5+3 )

2) lcm of 5 and 3 is 15 .

3) check ur assumption

4) u will get the numbers .

hope it helps !

❤️

~ananya

Answer 2

Step-by-step explanation:

Let the two numbers be x and y

Therefore

x + y = 8..... (1)

&

$\frac{1}{x} + \frac{1}{y} = \frac{8}{15} \\ \implies \frac{y + x}{xy} = \frac{8}{15} \\ \implies \frac{x + y}{xy} = \frac{8}{15}...(2) \\ from \: equations \: (1) \: and \: (2) \\ \frac{8}{xy} = \frac{8}{15} \\ \implies \: \frac{1}{xy} = \frac{1}{15} \\ \implies \:xy = 15 \\ now \\ (x - y)^{2} = (x + y)^{2} - 4xy \\ = (8)^{2} - 4 \times 15 \\ = 64 - 60 \\ \implies (x - y)^{2} = 4 \\ x - y = 2.....(3) \\ adding \: equations \: (1) \: and \: (3) \\ x + y = 8 \\ x - y = 2 \\ - - - - - \\ 2x = 10 \\ \implies \implies \: x = \frac{10}{2} \\ \implies \huge\fbox{x = 5} \\ \implies 5 + y = 8 \\ \implies \: y = 8 - 5 \\ \implies \huge\fbox {\: y = 3}$