ISI2017-MMA-10

Question

The inequality $\mid x^2 -5x+4 \mid > (x^2-5x+4)$ holds if and only if

• A. $1 < x < 4$
• B. $x \leq 1$ and $x \geq 4$
• C. $1 \leq x \leq 4$
• D. $x$ takes any value except $1$ and $4$

Answer 1

Answer = A

Comments

can you please give some explanation for getting answer A

Answer 2

X=2,3  satisfies the above inequality condition so answer is(D)

Comments

Ans should be option A as only  values between this 1<x<4 satisfies the inequality

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C not true because on keep either 1or 4 inequality is not satisfied as 0>0 is false

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ok , thanks :)

Answer 3

let us take an example to understand the problem ,if $\left | x \right |> 2$ then solution set of this inequality will be (2,infinity) union (-infinity,2) , similarly we will proceed for this $ x^2-5 x+4 $< -(x^2-5x+4) it implies (x-1)(x-4)<0 which has solution lies in 1<x<4 and the other part $ x^2-5 x+4  $> (x^2-5x+4) has no solution so finally we get option A.

Answer 4

Answer (A):

Case 1: If x$^{2}$-5x+4 > 0 then mod will open with postive sign

               Thus, |x$^{2}$-5x+4 | = x$^{2}$-5x+4 and hence not greater than

                hence case 1 is rejected.

Case 2: If x$^{2}$-5x+4 < 0 then mod will open with negative sign

                x$^{2}$-5x+4 < 0

              $\therefore$  (x – 4)(x – 1) < 0

               So x lies between 1 and 4

1 < x < 4