Question

giải pt sau: x + (x+1)\(\sqrt{x+3}\)=5

Answer 1

ĐKXĐ: x+3>=0

=>x>=-3

\(x+\left(x+1\right)\sqrt{x+3}=5\)

=>\(x+\sqrt{\left(x+3\right)\left(x+1\right)^2}=5\)

=>\(x+\sqrt{\left(x+3\right)\left(x^2+2x+1\right)}=5\)

=>\(x+\sqrt{x^3+2x^2+x+3x^2+6x+3}=5\)

=>\(x+\sqrt{x^3+5x^2+7x+3}=5\)

=>\(x-1+\sqrt{x^3+5x^2+7x+3}-4=0\)

=>\(\left(x-1\right)+\dfrac{x^3+5x^2+7x+3-16}{\sqrt{x^3+5x^2+7x+3}+4}=0\)

=>\(\left(x-1\right)+\dfrac{x^3-x^2+6x^2-6x+13x-13}{\sqrt{x^3+5x^2+7x+3}+4}=0\)

=>\(\left(x-1\right)+\dfrac{\left(x-1\right)\left(x^2+6x+13\right)}{\sqrt{x^3+5x^2+7x+3}+4}=0\)

=>\(\left(x-1\right)\left(1+\dfrac{x^2+6x+13}{\sqrt{x^3+5x^2+7x+3}+4}\right)=0\)

=>x-1=0

=>x=1(nhận)