the sum of two natural number is 8 determine the number if the sum of their reciprocal is 8/15
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harshald:
extreamly right answer
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Let the two natural numbers be x,y.
Given x+ y = 8
1/ x + 1/ y = 8/15
x+y/xy =8/15
From this xy =15
y = 15/x
Substitution of y value in x+ y = 8
=> x + 15/ x = 8
=> x²+15=8x
=> x²-8x+15=0
=> x²-3x-5x+15=0
=> x(x-3) - 5(x-3) =0
=> (x - 5) ( x-3) =0
=> x = 5 or 3
If we take value of x = 5 then y = 3
If we take value of x = 3 then y =5
Hence, Two natural numbers are 3,5
Hope it helps you!
Given x+ y = 8
1/ x + 1/ y = 8/15
x+y/xy =8/15
From this xy =15
y = 15/x
Substitution of y value in x+ y = 8
=> x + 15/ x = 8
=> x²+15=8x
=> x²-8x+15=0
=> x²-3x-5x+15=0
=> x(x-3) - 5(x-3) =0
=> (x - 5) ( x-3) =0
=> x = 5 or 3
If we take value of x = 5 then y = 3
If we take value of x = 3 then y =5
Hence, Two natural numbers are 3,5
Hope it helps you!
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