Correct Answer:
A. 7
The correct answer is 7. This is an algebraic problem that can be solved by squaring the given equation. We are given the equation x + 1/x = 3. To find x² + 1/x², we can square both sides of the original equation:
- (x + 1/x)² = 3²
Expanding the left side of the equation:
- (x + 1/x)² = x² + 2(x)(1/x) + (1/x)²
- = x² + 2 + 1/x²
Since 3² = 9, we can set the expanded form equal to 9:
- x² + 2 + 1/x² = 9
Now, to isolate x² + 1/x², subtract 2 from both sides of the equation:
- x² + 1/x² = 9 - 2
- x² + 1/x² = 7
Therefore, the value of x² + 1/x² is 7.
- Option B, 9, is incorrect because it implies simply squaring the right-hand side (3²) without accounting for the middle term (+2) when squaring the binomial (x + 1/x).
- Option C, 5, is incorrect. This value does not result from the correct algebraic manipulation of the given equation.
- Option D, 6, is incorrect. This might be a result of an arithmetic error, such as subtracting 3 instead of 2 from 9, or another miscalculation.