Решите неравенство [latex] log_{x} (sqrt{x^{2}+x-2 }+1)* log_{7}( x^{2}+x+1)= log_{x}3 [/latex]

[latex]Log_x( sqrt{x^2+x-2}+1)*Log_7(x^2+x+1)=Log_x3 [/latex][latex]ODZ: left { {{ sqrt{x^2+x-2}+1 extgreater 0} atop {x^2+x+1 extgreater 0}}atop {x^2+x-2 extgreater 0; x extgreater 0}}}} ight. [/latex][latex]ODZ: x extgreater 1[/latex][latex]Log_x( sqrt{x^2+x-2}+1)* frac{Log_x(x^2+x+1)}{Log_x7})=Log_x3 [/latex][latex]Log_x( sqrt{x^2+x-2} +1)*Log_x(x^2+x+1)=Log_x3*Log_x7 [/latex][latex] left { {{ sqrt{x^2+x-2}+1=3} atop {x^2+x+1=7}} ight. left { {{x^2+x-2=4} atop {x^2+x-6=0}} ight. left { {{x^2+x-6=0} atop {x^2+x-6=0} ight. x_1=2; x_2=-3 [/latex]т.к. x=-3 не подходит ОДЗОтвет х=2[latex] left { {{ sqrt{x^2+x-2}+1=7} atop {x^2+x+1=3}} ight. left { {{x^2+x-2=36} atop {x^2+x-2=0}} ight. [/latex]общих решений нетОтвет х=2