RMO Practice Problems - Algebra #3
Find the number of real numbers x that satisfy
2 x + 3 x − 4 x + 6 x − 9 x = 1
Try this set RMO Practice Problems .
The answer is 1.
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1 solution
Nice question.....loved to solve it....and nice solution!!
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Thanks sir.
a work of a true genius
Nice solution Dev! :D
Did it the same way! Nice solution by the way!
I solved the question to get 0 as the answer but it says 1 is the right answer can you please tell why.
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because it asks for the number of solutions
Zero is the value while the number of numbers (real) is 1. That is what the question is.
Did the exact same!!
how can we be so specific about how we need to solve? i first saw the question and thought it required higher knowledge . can you please solve for me x^(2x-1)=2 ??
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It's just about the observation. If you can figure out how a particular question is to be proceeded with, it only required simplification. This is the case for most of the RMO type problems.
As for the equation you gave, it has no integral solution. First, the negative integers are excluded as the exponent becomes negative. For x>2, x^(2x-1) >2. This implies x can lie only in 0,1,2. Checking cases, we can say there exist no integral solutions
kisiki aukat h to proper solution do x^(2x-1)=2 ka rational root
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It really isn't a polite way of asking someone to clear your query.........aukat km bat kahan se aayi.......
wtf I tried 0
Let 2 x = a and 3 x = b . After substitution, this equation becomes
( a − b ) 2 + ( 1 − a ) 2 + ( b − 1 ) 2 = 0
The only way the left-hand side is 0 is if both ( 1 − a ) and ( 1 − b ) are 0. Therefore, 2 x = 3 x = 1 , implying that x = 0 is the only solution. The number of solutions is 1.