Question

if x=ksquare and y=k is a solution of the equation x-5y+6=0 find the value of k?​

Answer 1

Answer:

x-5y+6=0

$x - 5y + 6 = 0 - - (1) \\ put \: x = {k}^{2} \: and \: y = k \: in \: equation(1) \\ {k}^{2} - 5k + 6 = 0 \\ {k}^{2} - (2 + 3)k + 6 = 0 \\ {k}^{2} - 2k - 3k + 6 \\ k(k - 2) - 3(k - 2) = 0 \\( k - 3)(k - 2) = 0\\ if \\ (k - 3) = 0 \\ k = 3 \\ and \: if \\ (k - 2) = 0 \\ k = 2$

Hope it helps you.

Answer 2

AnswEr:

It is given that x = k² and y = k is a solution of the equation x - 5y + 6 = 0.

Therefore,

$\qquad \sf \: {k}^{2} - 5k + 6 = 0 \\ \\ \\ \implies \qquad \sf \: {k}^{2} - 3k - 2k + 6 = 0 \\ \\ \\ \implies \qquad \sf \: k(k - 3) - 2(k - 3) = 0 \\ \\ \\ \implies \qquad \sf \: (k - 3)(k - 2) = 0 \\ \\ \\ \implies \qquad \sf \: k - 2 = 0 \: \: \: or \: \: \: k = 3 \\ \\ \\ \implies \qquad \sf \: k = 2 \: \: \: or \: \: k \: = 3$

Hence, if x = k² and y = k is a solution of the equation x - 5y + 6 = 0 then the value of k will be k =2, k = 3.