Question

a) \(\sqrt{x+8}=x+2\)
b) \(\sqrt{3+x}-2x=5+\sqrt{3+x}\)
c) \(\sqrt{5x+3}=3x-7\)
d) \(\sqrt{3x^2-2x-1}=3x+1\)
e) \(\sqrt{3x-5=4}\)
f) \(\sqrt{x^2-4}=x-1\)
g) \(\sqrt{x^2+x+1}=3-x\)
h) \(\sqrt{2x+2}=x-3\)

Answer 1

a. \(\sqrt{x+8}=x+2\)

đk x ≥ -2

⇔ \(\left(\sqrt{x+8}\right)^2\) = (x + 2 )²

⇔ x + 8 = x² + 4x + 4

⇔ x² + 3x - 4 = 0

⇔ (x - 1)(x + 4) = 0

⇔\(\left[{}\begin{matrix}x=1\\x=-4\left(L\right)\end{matrix}\right.\)

S = \(\left\{1\right\}\)

Answer 2

c: \(\Leftrightarrow\left\{{}\begin{matrix}x>=\dfrac{7}{3}\\9x^2-42x+49-5x-3=0\end{matrix}\right.\)

=>x>=7/3 và 9x^2-47x+46=0

=>\(x=\dfrac{47+\sqrt{553}}{18}\)

d: \(\left\{{}\begin{matrix}x>=-\dfrac{1}{3}\\3x^2-2x-1=9x^2+6x+1\end{matrix}\right.\)

=>x>=-1/3 và -6x^2-8x-2=0

=>x=-1/3

e: =>3x-5=16

=>3x=21

=>x=7

g: =>x<=3 và x^2+x+1=x^2-6x+9

=>x=8/7