If the sum of two natural number is 8 and the sum of their reciprocal is 8 upon 15 find the numbers
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Let the two numbers be x and y.
given,
x+y = 8 → (1)
from (1) x = 8-y
1/x +1/y = 8/15 →(2)
simplifying (2)
y+x/xy = 8/15
substituting the values we get,
8/(8-y)y = 8/15
8/8y-y² =8/15
15*8 = 8(8y-y²)
120 = 64y-8y² →(3)
dividing (3) by8 we get,
8y-y² = 15
⇒-y²+8y = 15
on solving this eqn we get,
y = 3 or 5
acc to the qstn,
x+y = 8
(if y= 3)
x+3 = 8
x=5
∴ the two numbers are 5 and 3
Hope it helps... :)
given,
x+y = 8 → (1)
from (1) x = 8-y
1/x +1/y = 8/15 →(2)
simplifying (2)
y+x/xy = 8/15
substituting the values we get,
8/(8-y)y = 8/15
8/8y-y² =8/15
15*8 = 8(8y-y²)
120 = 64y-8y² →(3)
dividing (3) by8 we get,
8y-y² = 15
⇒-y²+8y = 15
on solving this eqn we get,
y = 3 or 5
acc to the qstn,
x+y = 8
(if y= 3)
x+3 = 8
x=5
∴ the two numbers are 5 and 3
Hope it helps... :)
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