# The sum of two numbers is 15 and the sum of their reciprocal is 3/10. Find the numbers.

2
by dweejareddy

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by dweejareddy

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=>A+B=15 .............(1)

and

1/A +1/B=3/10

⇒(A+B)/AB = 3/10

from (1)

(A+B)/AB = 15/AB

⇒15/AB = 3/10

⇒AB = 50 ............(2)

solving (1) and (2)

A = 10 and B = 5

or

A = 5 and B = 10

X+Y=15.....................(1)

SUMOF RECIPROCAL OF THAT TWO NUMBER=>1/X+1/Y=3/10

=>X+Y/XY = 3/10

=>X+Y = 3XY/10...........................(2)

SUBSTITUTE X+Y VALUE IN (2)

=>15*10 = 3XY

=>150 = 3XY

=>50=XY

=>Y=50/X..........................(3)

(3) IN (1)

X+50/X=15

X²+50=15X

X²-15X+50=0

X²-5X-10X+50=0

X(X-5)-10(X-5)=0

(X-10)(X-5)=0

X=10 AND X=5

SUBSTITUTE X VALUE IN (1)

10+Y=15 AND 5+Y=15

Y=5 AND Y=10