\(\left(\dfrac{\sqrt{a}-1}{\sqrt{a}+1}+\dfrac{\sqrt{a}+1}{\sqrt{a}-1}\right)\left(1-\dfrac{2}{a+1}\right)^2\)
\(=\left(\dfrac{\left(\sqrt{a}-1\right)^2}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}+\dfrac{\left(\sqrt{a}+1\right)^2}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}\right)\left(1-\dfrac{4}{a+1}+\dfrac{4}{\left(a+1\right)^2}\right)\)
\(=\left(\dfrac{\left(\sqrt{a}-1\right)^2+\left(\sqrt{a}+1\right)^2}{a-1}\right).\left(\dfrac{\left(a+1\right)^2}{\left(a+1\right)^2}-\dfrac{4\left(a+1\right)}{\left(a+1\right)^2}+\dfrac{4}{\left(a+1\right)^2}\right)\)\(=\dfrac{a-2\sqrt{a}+1+a+2\sqrt{a}+1}{a-1}.\dfrac{\left(a+1\right)^2-4\left(a-1\right)+4}{\left(a+1\right)^2}\)
\(=\dfrac{2a+2}{a-1}.\dfrac{a^2+2a+1-4a-4+4}{\left(a+1\right)^2}\)
\(=\dfrac{2\left(a+1\right)\left(a^2-2a+1\right)}{\left(a-1\right)\left(a+1\right)^2}\)
\(=\dfrac{2\left(a+1\right) \left(a-1\right)^2}{\left(a-1\right)\left(a+1\right)^2}\)
\(=\dfrac{2\left(a-1\right)}{a+1}\)
Cho PT x2 - 2mx + 2m - 1 = 0
Đặt A = 2(x12 + x22) - 5x1x2
a) Chứng minh rằng A = 8m2 - 18m + 9
b) Tìm m để đạt GTNN
\(\left(\sqrt{\dfrac{1}{3}}-\sqrt{\dfrac{4}{3}}+\sqrt{3}\right):\sqrt{3}\)
\(\left(2+\sqrt{5}+\sqrt{3}\right)\left(2+\sqrt{5}-\sqrt{3}\right)\)
1. Rút gọn biểu thức sau:
a, \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
b, (\(\sqrt{3}-1\)) \(\sqrt{6+2\sqrt{2}\sqrt[]{3}-\sqrt{\sqrt{2}}+\sqrt{12}+\sqrt{18-128}}\)
Giải hệ phương trình
\(3x^2+2y^2-4xy+x+8y-4=0\)
\(x^2-y^2+2x+y-3=0 \)
Tính giá tri của biểu thức : .
A= x3 - 30x2 - 31x +1 tại x = 31
\(\sqrt{x+3}-\sqrt{2-x}=1\)
Giải hệ PT: \(\left\{{}\begin{matrix}x^2+y^2+\dfrac{2xy}{x+y}=1\\\sqrt{x+y}=x^2-y\end{matrix}\right.\)
Cho \(\Delta\) ABC vuông tại A, đường cao AH. Tính HB, biết :
a, BC = 5cm ; AH = \(\sqrt{6}\) cm
b, AB= 6cm ; HC = 5cm
[căn 12 - 2 căn 75]. căn 3
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