Question

Lg x²+ lg (x+10)² = 2lg 11

Answer 1

$\lg x^2+\lg (x+10)^2 =2\lg 11\\\\\lg x^2(x+10)^2=\lg 11^2\\\\(x(x+10))^2=11^2\\\\|x(x+10)|=11\\\\\\ \left[\begin{array}{ccc} \left \{ {{x(x+10)=11} \atop {x(x+10) \geq 0}} \right.\\ \\ \left \{ {{x(x+10)=-11} \atop {x(x+10)\ \textless \ 0}} \right. \end{array}\right=\ \textgreater \ \left[\begin{array}{ccc} \left \{ {{x^2+10x-11=0} \atop {x(x+10) \geq 0}} \right.\\ \\ \left \{ {{x^2+10x+11=0} \atop {x(x+10)\ \textless \ 0}} \right. \end{array}\right=\ \textgreater$ 


$\left[\begin{array}{ccc} \left \{ {{(x+11)(x-1)=0} \atop {x\in(-\infty;-10]U[0;+\infty)}} \right.\\ \\ \left \{ {{(x-(-5-\sqrt{14}))(x-(-5+\sqrt{14}))=0} \atop {x\in(-10;0)}} \right. \end{array}\right=\ \textgreater \ \left[\begin{array}{ccc}x_1=-11\\x_2=1\\x_3=-5-\sqrt{14}\\x_4=-5+\sqrt{14}\end{array}\right$