1) Giải phương trình
a) \(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}=\frac{x+3}{2}\)
b) \(x^2-8x+18=\sqrt{2x-7}+\sqrt{9-2x}\)
2) rút gọn
a) M = \(\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{3}-2\right)\sqrt{\sqrt{3}+2}\)
b) N= \(\sqrt{10+\sqrt{27}+\sqrt{40}+\sqrt{60}}\)
c) C = \(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\)
1. a) Ta có: \(\sqrt{x+2\sqrt{x-1}}+\sqrt{x+2\sqrt{x-1}}=\frac{x+3}{2}\)
\(\Leftrightarrow\sqrt{x+2\sqrt{x-1}}.2=\frac{x+3}{2}\)
\(\Leftrightarrow\sqrt{x+\sqrt{2-1}}.2=\frac{x+3}{2}\)
Bạn tự khai triển ra nha!
b) Tương tự
2) Tự làm
Ps: Ms lớp 6 nên chỉ làm được như vậy thôi! Bạn tự khai triển thành bài nhé!
1)
a) đk x>=1
\(\Leftrightarrow\sqrt{x-1+2\sqrt{x-1}+1}+\sqrt{x-1-2\sqrt{x-1}+1}=\frac{x+3}{2}\)
\(\Leftrightarrow\sqrt{\left(\sqrt{x-1}+1\right)^2}+\sqrt{\left(\sqrt{x-1}-1\right)^2}=\frac{x+3}{2}\)
\(\Leftrightarrow\left|\sqrt{x-1}+1\right|+\left|\sqrt{x-1}-1\right|=\frac{x+3}{2}\)
\(\Leftrightarrow\sqrt{x-1}+1+\left|\sqrt{x-1}-1\right|=\frac{x+3}{2}\)
vs x>=2
thì pt có dạng
\(\sqrt{x-1}+1+\sqrt{x-1}-1=\frac{x+3}{2}\)
\(4\sqrt{x-1}=x+3\)
\(16x-16=x^2+6x+9\)
\(x^2-10x+25=0\)
x=5(tm)
vs 0<=x<1
pt \(2=\frac{x+3}{2}\)
\(x+3=4\)
\(x=1\)
b2
ý c
\(C=\sqrt{\frac{8+2\sqrt{7}}{2}}-\sqrt{\frac{8-2\sqrt{7}}{2}}=\frac{\sqrt{7}+1-\sqrt{7}+1}{\sqrt{2}}=\frac{2}{\sqrt{2}}=\sqrt{2}\)
