Tinkutara Equation Editor: Math Forum Question #: 149040


Question Number 149040 by mathdanisur last updated on 02/Aug/21
${ ((x^2 +xy=4x)),((y^2 +xy=4y)) :} ⇒ log_(16) ^((x_1 +y_1 +x_2 +y_2 )) = ?$
	Answered by bramlexs22 last updated on 02/Aug/21
	$(1)+(2)⇔x^2 +2xy+y^2 =4(x+y) ⇒(x+y)^2 =4(x+y);(x+y)(x+y−4)=0 case(1)⇒x=−y ⇒x^2 −x^2 =4x ⇒ { ((x_1 =0)),((y_1 =0)) :} case(2)x=4−y ⇒x(x+y)=4x ; 4x=4x →x_2 =λ ,y_2 =4−λ then log _(16) (x_1 +y_1 +x_2 +y_2 )=log _(16) (0+λ+4−λ) =log _(16) (4)=(1/2)$
	Commented bymathdanisur last updated on 02/Aug/21