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Grade: 11

                        

If x 3/4(log 3 X)^2 + log 3 X - 5/4 = root 3. then x has a) one negative integral value b) two irrational value c) two positive rational value d) none of these

11 years ago

Answers : (1)

pratham ashish
9 Points
							Hi,

just take the log base 3 of both side and put log(x)to the base 3 = some t

now the eqn will  
                  => {3/4(t)^2 +t - 5/4}t =1/2

by putng 0 & 1 u'll cm to now that one root is one

then rearrange the eqn like 3(t)^3 +4(t)^2 -5t -2 =0

now 1 is a root then divide it by (t-1) u'll get:

                                         3(t)^2+7t+2=0
                                        => (3t+1)(t+2)=0
                                        => t = -2 , -1/3
                                    => x = (3)^1, (3)^-2 ,(3)^-1/3
                                    => x= 3, 1/9,  1/cube root of(3)
   
                           3 & 1/9 r rational & +ve but -2 is _ve integral value 

       Hence option a) & c) r correct

hav gd lk
						
11 years ago
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