Question

3(y – 5)2 + 5y =(2y - 3)2 – (y + 1)2+1​

Answer 1

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✪ 3(y-5)²+5y=(2y-3)²-(y+1)²+1

$\: \\ \implies \bf{3( {y - 5})^{2} + 5y = {(2y - 3)}^{2} - {(y + 1)}^{2} + 1}$

$\: \\ \implies \bf{3( {y}^{2} + 25 - 10y )+ 5y = {4y}^{2} + 9 - 12y - ( {y}^{2} + 2y + 1) + 1}$

$\: \\ \implies \bf{3 {y}^{2} + 75 - 30y + 5y = 4 {y}^{2} - 12y + 9 - {y}^{2} - 2y - 1 + 1}$

$\: \\ \implies \bf{ {3y}^{2} - 27y + 75 = 3 {y}^{2} - 14y + 8}$

$\: \\ \implies \bf{3 {y}^{2} - 27y + 75 - {3y}^{2} + 14y - 8 = 0}$

$\: \implies \bf{ - 27y + 14y + 75 - 8 = 0}$

$\: \implies \bf{ - 13y + 67 = 0}$

$\: \implies \bf{y = \frac{ 67}{13}}$