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The difference of two natural numbers is 5 and the difference of their reciprocals is 5/14. Find the numbers.
Solution
Let the two natural numbers be x and y A/q
y−x=5.....(1)
1x−1y=514....(2) From( 1.)
y=x+5
Putting the value of y in eqn. (2)1x−1x+5=514=>x+5−xx(x+5)=514=>5x2+5x=514=>x2+5x−14=0=>x2+(7−2)x−14=0=>x2+7x−2x−14=0=>x(x+7)−2(x+7)=0=>(x+7)(x−2)=0
Either x+7=0
=>x=−7Not acceptable because -7 is not natural number Or,
x−2=0=>x=2So, the first number is 2
Other number =x+5=2+5=7
so the numbers are 7 and 2
Mathematics
Secondary School Mathematics X
Standard X
1