IIT JEE , AIEEE Forum - Mathematics , Algebra

dixit_se

solve
___x-1______ <1
x²-4x+3

nivedh_89

(x-1)/(x-3)(x-1)<1

therefore
1/(x-3)<1
hence
x-3>1
x>4................!!!!!!!!!!!!
oh yes........
x<4 but x

{1,3}

metal

Hey,

nivedh you are wrong. (x-3) can be greater than zero or less than it, there are two possibilities.

If x-1=0 , then the inequality holds true and x=1. Else

if x-1 is not equal to zero,

x²-4x+3=(x-1)(x-3) and the (x-1) in the numerator and denominator cancel each other.

So, weget 1/(x-3) < 1. [ineq 1]

Now, if x-3>=0 i.e. x>=3,

from [ineq 1] we get x-3>1, i.e. x>4.

combining both we get x>4.

Again if x-3<0, i.e. x<3 ,

from [ineq 1] we get x-3<1 i.e. x<4.

combining both we get x<4.

So the answer is (x<4)U(x=1)U(x>4)

Please do rate me.

nivedh_89

x cannot b equal 2 1 nor can it b equal 2 3................!!!!!!!!!!!

sankydreams

1/(x-3)<1
1/(x-3) - 1 < 0
(4 - x) / (x-3)<0
(x - 4) / ( x-3) > 0
Now apply wavy curve method and get ans as (-infinity,3)U(4,infinty)
rate if this helps u...

rini

the ans should be ..

x= R - (3,4) - {1}

metal

Nivedh, why can't x be 1?

put x=1.

the numerator becomes zero.

So,the whole L.H.S becomes zero, which is obviously less than 1.

Got it????????!!!!!!!.

spideyunlimited

(x-1) / (x-3)(x-1)
1/(x-3)<1 provided x not = 1 we have cancelled out (x-1)
1/(x-3) - 1 < 0
(4 - x) / (x-3)<0
(x - 4) / ( x-3) > 0

x E (-inf, 3) U (4, +inf) ~ {1}

*PLZ RATE*

spideyunlimited

metal!!!!!! u cant put x = 1... u will get 0 in denominator also... not defined buddy

akku

ans: x

(-

,3)

(4,

)-{1}
soln:
bringing 1 2 the LHS
-X^2+5X-4/(X-1)(X-3)<0
MULIPLY BY - AND REVERSE SIGN OF INEQUALITY
(X^2-5X+4)/(X-1)(X-3)>0
(X-1)(X-4)/(X-1)(X-3)>0
X is NOT = 1 as fn will b undefined
(x-3)(x-4)>0
x belongs to (-inf , 3) U(4, inf)-{1}
P.S. X is same as x(pls dont mind the capital fonts)

metal

Got it, spidey,x is not = 1.

Then the correct answer is (-infinity,4)U(4,infinity)

please rate.

shohitaa

see on factorising we get

(x-1)/(x-1)(x-3)<1

so we get (1/(x-3))-1<0

on solving:
(4-x)/(x-3)<0

taking -1 common we get
x-4/x-3>0
so finally we get
by wavy curve method

x belongs to (-inf,3)U(4, inf)

spideyunlimited

metal!!! it is (-inf, 3) U (4, +inf) ~ {1}

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