Question

If x = - 2 and x2 + y2 + 3xy = -5 , then find y.

Answer 1

$\bf \large \underline{Given:}\\\\\bullet \rm{x = -2}\\\\\bullet \rm{x^{2} + y^{2} + 3xy = -5}\\\\\\\bf \large \underline{To\: find:}\\\\\star \sf{Value \: of \: y}\\\\\\\\\bf \large \underline{Method:}\\\\\rm{ Substitute \: value \: of\: x \:}\\\\\rm{x^{2} + y^{2} + 3xy = -5}\\\\\\\leadsto \sf{(-2)^{2} + y^{2} + 3(-2)y = -5}\\\\\\\longrightarrow \sf{4 + y^{2} - 6y = -5}\\\\\\\dashrightarrow \sf{y^{2} - 6y = -5 - 4}$

$\longrightarrow \sf{y^{2} - 6y = -9}\\\\\\\longrightarrow \sf{y^{2} - 6y + 9 = 0}\\\\\\Factorise \: the \: above \: Equation:\\\\\implies \sf{y^{2} - 3y - 3y + 9 = 0}\\\\\\\implies \sf{y(y - 3) - 3(y - 3)=0}\\\\\\\implies \sf{(y - 3)(y - 3) = 0}\\\\\\\implies \sf{(y - 3)^{2} = 0}\\\\\\\implies \sf{y - 3 = 0}\\\\\\\longrightarrow \boxed{\bf{\huge{y = 3}}}$