- #1
solakis1
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find A,B,C such that:
ABC= A!+B!+C!
ABC= A!+B!+C!
very good but can you explicity mention which are the theorem ,definitions or axiom used to solve the above?kaliprasad said:Because this is a 3 digit number each digit shall be < 7 as 7! is a 4 digit number that is 5040
Now no digit can be 6 because 6! = 720 so abc >700 so aother digit becomes 7
Largest digit has be 5 because if largest digit is 4 or more we have $ABC \le 72( 3 * 4!)$
So one digit is 5
Now 5!= 120
2 digits cannot be 5 because 5! + 5! = 240 and one dgit has to be 2 and it does not satisfy.
So we have 1 digit 5 and anothee digit A = 1.
B cannot be 5 because then largest C is 4 and sum <= 145 but b =5 makes abc > 150
So C is 5 and we have 100 + 10 * B + 5 = 1 + B! + 120 $ but tying different values B = 4 so number 145
solakis said:very good but can you explicity mention which are the theorem ,definitions or axiom used to solve the above?
The factorial equation is a mathematical equation used to calculate the product of a given number and all the smaller whole numbers before it. It is represented by an exclamation mark (!) after the number, for example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
To find the values of A, B, and C in a factorial equation, you will need to have a system of equations with three unknowns. You can then solve for these unknowns using algebraic methods such as substitution or elimination.
Yes, you can use a calculator to solve for A, B, and C in a factorial equation. Most scientific calculators have the ability to solve systems of equations, making it easier to find the values of these unknowns.
In a factorial equation, A, B, and C represent the coefficients of the terms in the equation. These coefficients help to determine the value of the factorial equation and can also be used to find the general term in a factorial sequence.
Yes, the factorial equation has many real-life applications, such as in probability and statistics, where it is used to calculate the number of possible outcomes in a given scenario. It is also used in computer science and engineering for tasks such as data compression and encryption.