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If x3/4(log3X)^2 + log3X - 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

7 years ago


Answers : (1)


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:

=> (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
7 years ago

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