Решить уравнение [latex] \sqrt{2x-3}+ \sqrt{2x-5}= \sqrt{5x-12}+ \sqrt{5x-14} [/latex]

[latex] \sqrt{2x-3} + \sqrt{2x-5} = \sqrt{5x-12} + \sqrt{5x-14} [/latex] [latex] \sqrt{2x-3} - \sqrt{5x-12} = \sqrt{5x-14} - \sqrt{2x-5} [/latex] [latex]( \sqrt{2x-3} - \sqrt{5x-12} )( \sqrt{2x-3}+ \sqrt{5x-12} )= \sqrt{2x-3}^2- \sqrt{5x-12}^2 [/latex] [latex] \sqrt{2x-3}^2- \sqrt{5x-12} ^2= \sqrt{5x-14}^2 - \sqrt{2x-5} ^2 [/latex] [latex]2x-3-5x+12=5x-14-2x+5[/latex] [latex]2x+2x-5x-5x=-14+5+3-12[/latex] [latex]-6x=-18[/latex] x=3 Проверка: [latex] \sqrt{2*3-3} + \sqrt{2*3-5} = \sqrt{5*3-12} + \sqrt{5*3-14} [/latex] [latex] \sqrt{3} + 1= \sqrt{3} +1[/latex]