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Let S(n) denotes the number of ordered p...

Let `S(n)` denotes the number of ordered pairs `(x,y)` satisfying `1/x+1/y=1/n,AA ,n in N` `S(10)` equals

A

S(3)+S(4)

B

S(5)+S(6)

C

S(8)+S(9)

D

S(1)+S(11)

Text Solution

Verified by Experts

The correct Answer is:
C
`because 6^(2)=2^(2)*3^(2)`
`impliesS(6)=3xx3=9 and 7^(2)impliesS(7)=3`
`thereforeS(6)+S(7)=12`
also, `8^(2)=2^(6)`
`impliesS(8)=7 and 9^(2)=3^(4) impliesS(9)=5`
`thereforeS(8)+S(9)=12`
`impliesS(6)+S(7)=S(8)+S(9)=12`.
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