Find the Value of k for which the Given Value is a Solution
Question:
Find the value of \(k\) for which the given value is a solution of the equation:
\[ x^2-x(a+b)+k=0 \]
Given, \[ x=a \]
Solution
Since \(x=a\) is a solution, it must satisfy the given equation.
Substituting \(x=a\) into the equation:
\[ a^2-a(a+b)+k=0 \]
\[ a^2-a^2-ab+k=0 \]
\[ -ab+k=0 \]
\[ k=ab \]
Answer
Therefore, the required value of \(k\) is
\[ \boxed{k=ab} \]
Hence, when \(k=ab\), the value \(x=a\) satisfies the equation \(x^2-x(a+b)+k=0\).