Question

Find the value of variable y using appropriate identity (y-5)2-(y-3)2=12
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Answer 1

`{(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 = ( - 4)/( - 4) \\ = \boxed{y = 1}`

y=1 is the right answer.

Answer 2

`\\\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`