Sqrt(x+10)-sqrt(x+3)=sqrt(4x-23)

ОДЗ: x+10≥0       x+3≥0       4x-23≥0            x≥-10           x≥-3          x≥5,75 x∈[5,75; +[latex]\infty[/latex]) [latex]\sqrt{x+10}-\sqrt{x+3}=\sqrt{4x-23} \\ (\sqrt{x+10}-\sqrt{x+3})^2=(\sqrt{4x-23} )^2 \\ x+10-2\sqrt{x+10}*\sqrt{x+3}+x+3=4x-23 \\ -2\sqrt{(x+10)(x+3)}=4x-23-x-10-x-3 \\ -2\sqrt{x^2+13x+30}=2x-36 \\ \sqrt{x^2+13x+30}=18-x \\ (\sqrt{x^2+13x+30})^2=(18-x)^2 \\ x^2+13x+30=324-36x+x^2 \\ 49x=294 \\ x=294:49 \\ x=6[/latex]