Question

Пожалуйста,помогите решить уравнение

Answer 1

$sqrt{2x-6} + sqrt{x+4} = 5, \ left { {{2x-6 geq 0,} atop {x+4 geq 0;}} right. left { {{x geq 3,} atop {x geq -4;}} right. x geq 3; \ sqrt{2x-6} = 5 - sqrt{x+4}, \ (sqrt{2x-6})^2 = (5 - sqrt{x+4})^2, \ 2x-6 = 5^2-2cdot5sqrt{x+4}+(sqrt{x+4})^2, \ 2x-6 = 25-10sqrt{x+4}+x+4, \ 10sqrt{x+4}=x+29-2x+6, \ 10sqrt{x+4}=35-x, \ 35-x geq 0, x leq 35, \ 3 leq x leq 35;$
$(10sqrt{x+4})^2=(35-x)^2, \ 100(x+4)=1225-70x+x^2, \ x^2-70x+1225=100x+400, \ x^2-70x+1225-100x-400=0, \ x^2-170x+825=0,\ D_{/4}=(-85)^2-825=7225-825=6400=80^2, \ x=85pm80, \ x_1=5, x_2=165. \ x=5.$