Question

Sum of to numbers is 18. The sum of their reciprocals is 1/4. Find the numbers

Answer 1

Hiiii friend,


Let the numbers be X and Y.

According to question,


X + Y = 18.......(1)


reciprocal of X is 1/X and reciprocal of Y is 1/Y.


According to question,


1/X+ 1/Y = 1/4

Y+ X/XY = 1/4

4(Y+X) = XY

4Y + 4X = XY........(2)


From equation (1) we get,

X + Y = 18

X = 18-Y......(3)


Put

4X + 4Y = XY

4 × (18-Y) + 4Y = (18-Y) × Y.



72 - 4Y + 4Y = 18Y - Y².

Y²-18Y +72 = 0

Y²-12Y-6Y +72 = 0


Y(Y-12) -6(Y-12) = 0

(Y-12) (Y-6) = 0

(Y-12) = 0 OR (Y-6) = 0


Y = 12 OR Y = 6


PUTTING Y = 12 in equation (3)


X = 18-Y = 18-6 = 12.


Hence,


The numbers are 12 and 6



HOPE IT WILL HELP YOU....... :-)

Answer 2

Hello friend

Good morning

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Your answer is given in the attachment i hope it will help you

Have. A great day

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