5,513 views
33 votes
33 votes

If $x$ is real and $\mid x^2-2x+3 \mid = 11$, then possible values of $\mid -x^3+x^2-x\mid$ include

  1. $2, 4$
  2. $2, 14$
  3. $4, 52$
  4. $14, 52$

4 Answers

Best answer
35 votes
35 votes
$x^2 - 2x + 3 = 11$ OR $x^2 -2x+3 = -11$
$($Any one of them can be correct because of $\text{mod})$

Lets take first one:
$x^2 - 2x + 3 = 11$
$\implies x^2 - 2x - 8 = 0$
$\implies (x-4) (x+2) =0$
$\implies x= 4 \text{ or } x = -2.$

Now put these values of $x$  in the given equation $\mid -x^3+x^2 -x\mid $

for $x= 4,$ we will get $\mid -64+16-4\mid \quad= 52.$
for $x = -2,$ we will get $\mid 8 + 4 + 2 \mid \quad= 14.$

So, answer is $D.$
edited by
2 votes
2 votes
d )

x=-2 ans is 14

x=4 ans is 52
0 votes
0 votes
| x2 – 2x + 3 | = 11  

To solve this we should know that ,  

if |x| = n then x=+n and x= -n  

So, we get 2 equations

Equation-1  

X2 –2x +3 = + 11    

X2 -2x –8 = 0  

X2 –4x+2x-8 = 0     X(x-4) +2(x-4) = 0  

X= -2 or x=+4  

Substitute the values in the given equation

|x3 + x2 –x|  

Subsitute x= -2: we get the value 14  

Substitute x=4: we get the value 52

 

Equation-2:  

x2- 2x +3 = -11

for this  

√b2−4ac <0

in question they mentioned x is real but here

roots are imaginary so , there will no real values

so we ignore this
Answer:

Related questions

23 votes
23 votes
9 answers
1
go_editor asked Sep 28, 2014
9,950 views
At what time between $6$ a. m. and $7$ a. m. will the minute hand and hour hand of a clock make an angle closest to $60^{\circ}$?$6: 22$ a.m.$6: 27$ a.m.$6: 38$ a.m.$6: 4...
19 votes
19 votes
3 answers
2
35 votes
35 votes
4 answers
3
Arjun asked Feb 14, 2017
8,851 views
The expression $\large \frac{(x+y) - |x-y|}{2}$ is equal to :The maximum of $x$ and $y$The minimum of $x$ and $y$$1$None of the above
6 votes
6 votes
2 answers
4
makhdoom ghaya asked Jan 25, 2017
1,968 views
If $\mid 9y-6 \mid = 3$, then $y^{2}-\dfrac{4}{3}y$ is .$0$$+\dfrac{1}{3}$$-\dfrac{1}{3}$undefined