Question

sqrt{x-4} - sqrt{6-x} = 2

Answer 1

ОДЗ: x-4>0         6-x>0
         x>4            x<6
$sqrt{x-4}-sqrt{6-x}=2\sqrt{x-4}=2+sqrt{6-x}\(sqrt{x-4})^2=(2+sqrt{6-x})^2\x-4=4+4sqrt{6-x}+6-x\2sqrt{6-x}=x-7\(2sqrt{6-x})^2=(x-7)^2\4(6-x)=x^2-14x+49\x^2-14x+49-24+4x=0\x^2-10x+25=0\(x-5)^2=0\x-5=0\x=5$