Question:
If
\[
\begin{bmatrix} x + y & 2 \\ 5 & xy \end{bmatrix} = \begin{bmatrix} 6 & 2 \\ 5 & 8 \end{bmatrix},
\]
then the value of
\[
\left(\frac{24}{x} + \frac{24}{y}\right)
\]
is:
If
\[ \begin{bmatrix} x + y & 2 \\ 5 & xy \end{bmatrix} = \begin{bmatrix} 6 & 2 \\ 5 & 8 \end{bmatrix}, \]
then the value of\[ \left(\frac{24}{x} + \frac{24}{y}\right) \]
is:Show Hint
To solve matrix element problems, equate corresponding elements and solve algebraically using known identities.
Updated On: Feb 25, 2026
- \( 7 \)
- \( 6 \)
- \( 8 \)
- \( 18 \)
Show Solution
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The Correct Option is D
Solution and Explanation
Step 1: Equate corresponding elements of the matrices.
\[
x + y = 6, \quad xy = 8
\]
Step 2: Solve for the required expression.
We need to evaluate:
\[
\frac{24}{x} + \frac{24}{y} = 24 \left(\frac{1}{x} + \frac{1}{y}\right)
\]
Using the identity:
\[
\frac{1}{x} + \frac{1}{y} = \frac{x + y}{xy}
\]
Substituting values:
\[
\frac{1}{x} + \frac{1}{y} = \frac{6}{8} = \frac{3}{4}
\]
Step 3: Final calculation.
\[
\frac{24}{x} + \frac{24}{y} = 24 \times \frac{3}{4} = 18
\]
Final Answer:
\[
\boxed{18}
\]
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