Hey guys forgot mathematical induction I knew in class 9..............
If y is a number obtained from x by rearranging the digits of x , and provided that :
x+y = 10^200
Prove that x is divisible by 10.
Note that x and y are natural numbers.
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Any class 12 or 11 student or a good student plz help me if you know anything about mathematical induction.
Any questions I can welcome but ask in comments only...
Answers
x + y = 10^200
Let last digits be s and t .
s + t + 10 * something = 10^200
= > s + t = 10^200 - 10*something
= > s + t is divisible by 10 .
s + t can be only 10 because s < 10 and t < 10 and s + t is divisible by 10 .
Suppose s + t = 10 , then we will have :
s + t + something = 10^200
= > s + t = 10^200 - 10*something
= > 10 = 10^200 - 10*something
= > 1 = 10^199 - something
= > something = 10^199 - 1 which is not divisible by 10 .
Hence there is a contradiction .
So s = 10 , t = 0 ?
This cannot be possible as s and t are the last digits and hence they should be less than 10 . They should be 0,1....9 .
So there exists no last digit .
x = 10 * second last digit + 100 * third last digit + ....
= > x is divisible by 10 off course .
Answer:
ok
Step-by-step explanation:
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