Question

If $x=k^2$ and $y=k$ is the solution of the equation $x-5y+6=0$, then the sum of values of $k$ is

• A. $5$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A

$5$

Explanation for the correct option:

Finding the sum of values of $k$.

Given,

$x=k^2$, $y=k$.

Equation : $x-5y+6=0$

We know that a solution satisfies the equation therefore putting the given values in the equation we get,

$$\begin{gathered} \Rightarrow x-5y+6=0 \\ \Rightarrow k^2-5k+6=0 \end{gathered}$$

Solving the quadratic equation :

$$\begin{gathered} \Rightarrow k^2-5k+6=0 \\ \Rightarrow k^2-3k-2k+6=0 \\ \Rightarrow k\times (k-3)-2\times (k-3)=0 \\ \Rightarrow (k-3)(k-2)=0 \\ \therefore k=3,2 \end{gathered}$$

Thus, the sum of the value of $k=2+3$, that is $5$.

Hence the correct option is A