SOLUTION: Find two numbers a and b such that the sum, product, and quotient of the two numbers are all equal.

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Question 3062: Find two numbers a and b such that the sum, product, and quotient of the two numbers are all equal.
Answer by kiru_khandelwal(79) About Me  (Show Source):
You can put this solution on YOUR website!
Let the two numbers be a and b
so a+b = ab = a/b
=> a+b = ab .....(1)
and ab = a/b....(2)
from equation (2)
ab^2 = a
=> b^2 = 1
=> b = +/-1
Now sbustituting b = 1 in equation (1)
=> a + 1 = a.....this is not possible as on adding 1 to ne number does not make it equal to itself
Now substituting b = -1 in equation(1)
=> a-1 = -a
=> 2a = 1
=> a = 1/2
so a = 1/2 and b = -1