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Best answer
18 votes
18 votes
$\text{Given }\left | -2X +9 \right | = 3,$

$\Rightarrow -2X +9 = 3 \text{ or } -\left (-2X +9 \right ) = 3,$

$\Rightarrow X = 3 \text{ or } X = 6,$

$\Rightarrow \left | -X \right |-X^{2} = \left | -3 \right |-3^{2} = -6 \text{ or } \left | -X \right |-X^{2} = \left | -6 \right |-6^{2} = -30,$

$\text{ Thus B is the correct option. }$
1 votes
1 votes

Answer : -30

Given :   |-2X + 9|=3

there will be 2 cases :

1. if (-2X+9) >= 0 ,                   2.   if (-2X + 9) < 0

   -2X+9 = 3                               -(-2X+9) = 3 

  -2X = -6                                      2X-9=3

    X = 3                                        X=12/2 = 6

Now, put these values in |-$X$| - $X^{2}$

1.    |-$3$|-$3^{2}$                                   2.    |-$6$|-$6^{2}$

       -(-3)-9                                              -(-6)-36

          3-9                                                  6-36

          -6                                                     -30

so, -30 matches here. 

0 votes
0 votes

Given  is |−2X+9|=3

removing mod operator with both sign
case 1 : if |−2X+9|>=0 mod will open with positive sign  i.e. (-2x+9)>=0 

                   hence x<4.5

              ⇒ (−2X+9)=3

              ⇒  x=3   (accepted)

|-X|-X^2 = |3|-9= -6

case 2 : if |−2X+9|<0 mod will open with negative sign  i.e. (-2x+9)<0

              hence x>4.5

              ⇒     (−2X+9)=-3   

              ⇒     x=6 (accepted)

now put value x=6 in 

|-X|-X^2 = |-6|-36= -30

option that matches is B


 Thus B is the correct option

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