Question

Решить уравнение

$sqrt{2x-3}+ sqrt{2x-5}= sqrt{5x-12}+ sqrt{5x-14}$

Answer 1

$sqrt{2x-3} + sqrt{2x-5} = sqrt{5x-12} + sqrt{5x-14}$
$sqrt{2x-3} - sqrt{5x-12} = sqrt{5x-14} - sqrt{2x-5}$
$( sqrt{2x-3} - sqrt{5x-12} )( sqrt{2x-3}+ sqrt{5x-12} )= sqrt{2x-3}^2- sqrt{5x-12}^2$
$sqrt{2x-3}^2- sqrt{5x-12} ^2= sqrt{5x-14}^2 - sqrt{2x-5} ^2$
$2x-3-5x+12=5x-14-2x+5$
$2x+2x-5x-5x=-14+5+3-12$
$-6x=-18$
x=3
Проверка: $sqrt{2*3-3} + sqrt{2*3-5} = sqrt{5*3-12} + sqrt{5*3-14}$
$sqrt{3} + 1= sqrt{3} +1$