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5^x + (2✓3)^2x >=13^x , then solution set for x is.................

5^x + (2✓3)^2x >=13^x , then solution set for x is.................

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2 Answers

Divyanshu
16 Points
5 years ago
5^x+(2√3)^x=13^x
5^x+12^x=13^x
5²+13²=13²
Now,if x=2 then,5²+12²=13²,which is true.(by fermat last theorem,we have no existence of x as an  integral value greater than 2 such that 
a^x+b^x=c^x
Also,for x=0,1 given equation is not satisfied.
Hence,in given equation integral value of x is 2 only.
Divyanshu
16 Points
5 years ago
5^x+(2√3)^2x=13^x
5^x+12^x=13^x
If x=2 then,5²+13²=13²,which is true.
Now,by fermat laat theorem,we have no existence of x as an integral value greater than 2 such that
a^x+b^x=c^x 
Also,for x=0,1 the given equation is not satisfied
Hence,in the given equation integral value of x is 2 only.

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