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If $x = k 2$ and $y = k$ is a solution of the equation $x − 5 y + 6 = 0$ , then the values of k are:

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2,3

3,4

1,2

3,5

answer is A.

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Detailed Solution

Given

x = k 2

y = k

and equation

x − 5 y + 6 = 0

.
Substitute

(x, y) = k 2, k

in the given equation.

⇒ k 2 − 5 k + 6 = 0 ⇒ k 2 − 2 k − 3 k + 6 = 0 ⇒ k (k − 2) − 3 (k − 2) = 0 ⇒ (k − 2) (k − 3) = 0 ⇒ k − 2 = 0, k − 3 = 0 ⇒ k = 2, k = 3

Therefore,

k = 2, 3

.
Hence, option (1) is correct.

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