Question

Find the value of variable y using appropriate identity (y-5)2-(y-3)2=12 ​

Answer 1

Answer:

${(y - 5)}^{2} - {(y - 3)}^{2} = 12 \\ = ( {y}^{2} - 10y + 25) - ( {y}^{2} - 6y + 9) = 12 \\ = {y}^{2} - 10y+ 25 - {y}^{2} + 6y - 9 = 12 \\ = - 4y + 16 = 12 \\ = - 4y = 12 - 16 \\ = - 4y = - 4 \\ = y = \frac{ - 4}{ - 4} \\ = \boxed{y = 1}$

y=1 is the right answer.

Answer 2

Answer:

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow (y-5)2-(y-3)2=12$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow 2y-10-2y-6=12$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow 2y-2y-10-6=12$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow -16=12$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow y's\:value\:is\:undefined$