GATE Chemical 2013 | Question: 64

Question

If $|-2x+9| = 3$ then the possible value of $|-X|-X^2$ would be:

• A. $30$
• B. $-30$
• C. $-42$
• D. $42$

Answer 1

| −2x + 9 | = 3

Case 1:
−2x + 9 = 3
−2x = −6
x = 3

Case 2:
−2x + 9 = −3
−2x = −12
x = 6

Now expression:

| −x | − x² = |x| − x²

For x = 3:
|3| − 9 = 3 − 9 = −6

For x = 6:
|6| − 36 = 6 − 36 = −30