Question

1. the difference of the two number is 4 .if the difference of their reciprocals is 4/21, find the two numbers.

2. the sum of two number is 18 and the sum of their reciprocal is 1/4 find the numbers

Answer 1

☆hey friend !!!☆

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here is your answer ☞
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let's the 1st number is = x

and, 2nd number is = y

Now, according to your question

$= > \: x - y = 4..............eq _{1} \\ \\ again \: question \: says \\ \\ = > \: \frac{1}{y} - \frac{1}{x} = \frac{4}{21} \\ \\ = > \: \frac{x - y}{xy} = \frac{4}{21} \\ \\ plug \: the \: valu e \: x - y = 4 \\ we \: get \: \\ \\ = > \frac{4}{xy} = > \frac{4}{21} \\ \\ = > \: xy \: = \: 21 \: \: ........eq _{2} \\ \\ we \: know \: that \\ \\ ({x + y})^{2} = ( {x - y)}^{2} + 4xy = 16 + 4(21) = 100 \\ \\ = > \: x + y = 10 \: ................eq _{3} \\ \\ adding \: eq _{1} \: and \: eq _{3} \\ we \: get \\ \\ = > \: 2x = 14 \\ x = 7..............answer \\ \\ and \\ \\ = > 7 - y = 4 \\ y = 3.............answer$
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hope it will help you ☺☺
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Devil_king ▄︻̷̿┻̿═━一

Answer 2

Hi user?!!!!

Let a>b

a−b=4

1b−1a=421

⟹a−bab=421

⟹ab=21

Now

(a−b)2=16

a2+b2–2×21=16

a2+b2=58

a2+b2+2ab=58+2×21

a+b=10

(a+b)+(a−b)=10+4

2a=14⟹a=7⟹b=3

7,3

Hope it helps u

#MarkAsBrainliest