Q.5 If |9y − 6| = 3, then y2 − 4y/3 is ________.
This multiple-choice question tests the understanding of absolute value equations
and algebraic simplification, commonly asked in competitive and board-level mathematics exams.
Solving the Equation
An absolute value equation of the form |A| = B (where B > 0) implies:
- A = B
- A = −B
For the given equation |9y − 6| = 3:
Case 1
9y − 6 = 3
⇒ 9y = 9
⇒ y = 1
Case 2
9y − 6 = −3
⇒ 9y = 3
⇒ y = 1/3
Both values satisfy the original equation.
Expression Evaluation
Substitute the values of y into the expression:
y² − (4y)/3
For y = 1
(1)² − (4 × 1)/3
= 1 − 4/3
= (3/3 − 4/3)
= −1/3
For y = 1/3
(1/3)² − (4 × 1/3)/3
= 1/9 − 4/9
= −3/9
= −1/3
In both cases, the value of the expression is the same.
Correct Answer
Correct Answer: −1/3
Options Analysis
| Option | Value | Correct? | Explanation |
|---|---|---|---|
| (A) | 0 | No | Neither substitution gives 0; both results are −1/3. |
| (B) | +1/3 | No | The obtained value is negative, not positive. |
| (C) | −1/3 | Yes | Matches the value obtained for both y = 1 and y = 1/3. |
| (D) | undefined | No | The expression is defined for all real y values used. |
