If yx02 4082= −; ; ;E E E, the value of x and y respectively are :(a) 1, -2 (b) -2, 1(c) 1, 2

Break Down the Problem

1. We need to solve for the values of $x$ and $y$ given the equation $yx^2 - 4082 = 0$, where $E$ represents some equality condition.

Relevant Concepts

2. Rearranging the equation, we have: $yx^2 = 4082$ This indicates that $y$ and $x$ are related through the product $yx^2$.

Analysis and Detail

3. We can analyze the given options by substituting the values of $x$ and $y$ from options (a), (b), and (c) into the rearranged equation:
   • For option (a): $(x, y) = (1, -2)$ $-2(1)^2 = -2 \quad \text{(not equal to 4082)}$
   • For option (b): $(x, y) = (-2, 1)$ $1(-2)^2 = 4 \quad \text{(not equal to 4082)}$
   • For option (c): $(x, y) = (1, 2)$ $2(1)^2 = 2 \quad \text{(not equal to 4082)}$

Verify and Summarize

4. After substituting all options into the equation, none resulted in the equality being satisfied ($yx^2 = 4082$). Since $y$ must be negative for any realistic values in this set-up to fit with negative results. Thus, without additional information, there is likely to be a typographical or contextual error in the problem statement.

Final Answer

None of the provided options satisfy the equation $yx^2 = 4082$. Additional context or correction may be needed for a valid solution.