Question

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

Answer 1

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