Mystery number
Number Theory
Level
1
There is a two digit number of which the sum of the two digits is the same as the product of the two digits. What is the number?
The answer is 22.
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well you can solve it using AM-GM inequality, if we consider the digits of the number to be a and b then by AM-GM inequality : a+b/2 is greater than or equal to square root of a * b or we can say that square root of a * b is less than equal to a+b/2 now the condition is a + b should be equal to a * b so , root of a * b = a + b/2 squaring both sides we get : 4 ab = a^2 + b^2 + 2ab simpliftying we get : (a-b)^2 = 0 therefore a = b and we use it in the given condition 2a = a^2 a = 2 therfore numbber = aa = 22