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if f:R gives Q(rational),g:R gives Q(rational) are two continuous functions suchthat (square root of 3)f(x)+g(x0=4 ,then (1-f(x)) 3 +(g(x)-3) 3 is equal to

if  f:R gives Q(rational),g:R gives Q(rational) are two continuous functions suchthat  (square root of 3)f(x)+g(x0=4 ,then (1-f(x))3  +(g(x)-3)3 is equal to
 

Grade:12

3 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
Dear student

Please ask the question in standard notation or attach the image of the question

Regards
Vikas TU
14149 Points
4 years ago
Dear student 
Question is not clear 
Please attach an image, 
We will happy to  help you 
Good Luck
Cheers
Aditya Gupta
2081 Points
4 years ago
dear student, the complete ignorance and lunacy shown by some members as Vikas and saurabh is totally uncalled for. In my earlier ans, he deems my ans as substandard. i dont like to be challenged by amateur and incompetent people like him in mathematics. he is a joke for a tutor.
CORRECT SOL:
sqrt(3)f(x)= 4 – g(x)
now, assume that f(x) is not zero at least for some x= x0
then, sqrt3= (4 – g(x0))/f(x0)
however, f and g can only take rational values, hence (4 – g(x0))/f(x0) must also be rational, which is impossible since sqrt3 is irrational.
hence, f(x)= 0 for all x
so that g(x)= 4 for all x.
so (1-f(x))3  +(g(x)-3)3= 1^3 + 1^3
= 2
KINDLY APPROVE :))

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