Question

12 lg(x-9)+lg√2x-1=1

Answer 1

$frac{1}{2} lg(x-9)+lgsqrt{2x-1}=1;Rightarrow D(f):x textgreater 9.\ lgsqrt{x-9}+lgsqrt{2x-1}=1;\ lgsqrt{(x-9)(2x-1)}=lg 10;\ sqrt{(x-9)(2x-1)}= 10;quad (x-9)(2x-1)= 100;\ 2x^2-19x-91=0;,D=19^2-4cdot 2cdot(-91)=361+728=1089;\ sqrt{D}=33,,x_1=frac{19+33}{4}=13 textgreater 9,,x_2=frac{19-33}{4}=-3.5 textless 9.\ x=14.$