BT1 Thực hiện các phép tính
a.A=\(\sqrt{17-12\sqrt{2}}\)
b.B=\(\sqrt{4-2\sqrt{3}}+\sqrt{7-4\sqrt{3}}\)
c. C=\(\sqrt{63}-\sqrt{28}-\sqrt{7}\)
d.D=\(\frac{2}{\sqrt{3-1}}-\frac{2}{\sqrt{3+1}}\)
e. M=\(\left(\frac{1}{3-\sqrt{5}}-\frac{1}{3+\sqrt{5}}\right):\frac{5-\sqrt{5}}{\sqrt{5-1}}\)
BT2 Tìm GTLN,GTNN của biểu thức
a, P=\(x^2-10x+3\)
b.Q=\(-x^2+20x\)
c A=\(\frac{1}{81}x^2+x-10\)
d B=\(\frac{2016}{x^2+4x-3}\)
1) \(A=\sqrt{17-12\sqrt{2}}=\sqrt{\left(2\sqrt{2}-3\right)^2}=3-2\sqrt{2}\)
\(B=\sqrt{4-2\sqrt{3}}+\sqrt{7-4\sqrt{3}}=\sqrt{\left(\sqrt{3}-1\right)^2}+\sqrt{\left(\sqrt{3}-2\right)^2}\)
\(=\sqrt{3}-1+2-\sqrt{3}=1\)
\(C=\sqrt{63}-\sqrt{28}-\sqrt{7}=3\sqrt{7}-2\sqrt{7}-\sqrt{7}=0\)
\(D=\frac{2}{\sqrt{3}-1}-\frac{2}{\sqrt{3}+1}=\frac{2\left(\sqrt{3}+1\right)-2\left(\sqrt{3}-1\right)}{3-1}=\frac{4}{2}=2\)
\(M=\left(\frac{1}{3-\sqrt{5}}-\frac{1}{3+\sqrt{5}}\right):\frac{5-\sqrt{5}}{\sqrt{5}-1}=\frac{3+\sqrt{5}-3+\sqrt{5}}{9-5}.\frac{\sqrt{5}-1}{\sqrt{5}\left(\sqrt{5}-1\right)}=\frac{2}{4}=\frac{1}{2}\)
bạn khó bài nào mik lm cho chứ nhiều quá
2) Mình chỉ làm tắt thôi nhé :)
a) \(P=x^2-10x+3=\left(x^2-10x+25\right)-22=\left(x-5\right)^2-22\ge-22\)
b) \(B=-x^2+20x=-\left(x^2-20x+100\right)+100=-\left(x-10\right)^2+100\le100\)
c)\(A=\frac{1}{81}x^2+x-10=\frac{1}{81}\left(x^2+2.x.\frac{81}{2}+\frac{81^2}{4}\right)-\frac{121}{4}=\frac{1}{81}\left(x+\frac{81}{2}\right)^2-\frac{121}{4}\ge-\frac{121}{4}\)
d) \(B=\frac{2016}{x^2+4x-3}=\frac{2016}{\left(x^2+4x+4\right)-7}=\frac{2016}{\left(x+2\right)^2-7}\le\frac{-2016}{7}\)
