Đáp án:
Bài 1:
1)3√36 -1/5√625-√121
=18-5-11=2
2)√1/4 -1/3√9/16+15√25/64
=1/2-1/3.3/4+1/5.5/8
=3/8
3)√5-4√5+2√5
=-√5
4)(√5+1)²-(3√5-1)(√5+1)
=5+2√5+1-(15+3√5-√5-1)
=5+2√5+1-15-3√5+√5+1
=-8
5)(√x+2)(√x-3)-√x(√x-1)
=x-√x-6-x+√x
=-6
6) (√x-2)²-(√x+2)²
=x-2√x+4-x-2√x-4
=-4√x
7)√(2√2-3)²-√(1-2√2)²
=3-2√2-1+2√2
=2
8)√(5-2√3)²-√(13-4√3)
=5-2√3-√(2√3-1)²
=5-2√3-2√3+1
=6-4√3
Bài 2:
a)√(9x²)=15
⇔9x²=225
⇔x²=25
⇔x=5
b)√(4(x-3)²)-12=0
⇔2|x-3|=12
⇔|x-3|=6
⇔$\alpha$ \(\left[ \begin{array}{l}x-3=6\\x-3=-6\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=9\\x=-3\end{array} \right.\)
c)√(7(x²-4x+a))=3√7
⇔√(7(x-2)²)=3√7
⇔√7.|x-2|=3√7
⇔|x-2|=3
⇔\(\left[ \begin{array}{l}x-2=3\\x-2=-3\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=5\\x=-1\end{array} \right.\)
d)√(5x²+10x+5) -2√5=0
⇔√(x√5+√5)²=2√5
⇔|x√5+√5|=2√5
⇔\(\left[ \begin{array}{l}x√5+√5=2√5\\x√5+√5=-2√5\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=1\\x=-3\end{array} \right.\)
e)√(x²-3x+1)=x-2
Bình phương 2 vế
⇔x²-3x+1=x²-4x+4
⇔x=3
