Question

The sum of two number is 8. Determine the numbers if the sum of their reciprocals is 8/15​

Answer 1

Answer:the two numbers are 3and 5

Step-by-step explanation:

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Answer 2

Let the numbers be x and y .

According to question :

$x+y=8\\\\x=8-y----(1)$

also,

$\frac{1}{x}+\frac{1}{y} =\frac{8}{15}----(2)$

Put the value of x from (i) equation in (2) equation :

$\frac{1}{8-y}+\frac{1}{y}=\frac{8}{15}\\ \\\frac{y+8-y}{8y-y^2} =\frac{8}{15}\\\\8(8y-y^2)=15(8)\\\\8y-y^2=15\\\\y^2-8y+15=0\\\\y^2-3y-5y+15=0\\\\y(y-3)-5(y-3)=0\\\\(y-5)(y-3)=0\\\\y=5\\\\or\\\\y=3$

Put the value of y in (1) equation :

CASE I : If y = 5 ,

$x =8-5\\\\x=3$

CASE II : If y = 3 ,

$x = 8 - 3\\\\x = 5$

Hence , the two numbers are 3 and 5 or 5 and 3 .