(x-y)^3=x^3-y^3-3xy(x-y)
P^3=\(9+4\sqrt{5}-\left(9-4\sqrt{5}\right)-3\cdot P\cdot\sqrt[3]{\left(9+4\sqrt{5}\right)\cdot\left(9-4\sqrt{5}\right)}\)
=8\(\sqrt{5}\)-3*P*\(\sqrt[3]{81-80}\)
=8\(\sqrt{5}\)-3P
\(\Rightarrow\)P^3+3P-8\(\sqrt{5}\)=0
P=2,236067977
Giair phương trình:
1) \(\sqrt[5]{32-x^2}-\sqrt[5]{1-x^2}=4\)
2) \(\sqrt{x}+\sqrt[4]{20-x}=4\)
3) \(x^3+1=2\sqrt{3x-1}\)
4) \(\sqrt[3]{x-1}+3=\sqrt[4]{82-x}\)
5)
\(a.\left(x+3\sqrt{x}+2\right)\left(x+9\sqrt{x}+18\right)=168x\)
\(b.\sqrt{5x^2+14x+9}-\sqrt{x^2-x-20}=5\sqrt{x+1}\)
a) \(\dfrac{5-2\sqrt{ }5}{\sqrt{ }5-2}-\dfrac{11}{4+\sqrt{ }5} \)
b)\(\sqrt{9+4\sqrt{ }5-\sqrt{ }6-2\sqrt{ }5}\)
c)\(\sqrt{17-3\sqrt{ }32+\sqrt{ }17+\sqrt{ }32}\)
Thực hiện phép tính:
1)A=\(\left(\dfrac{1}{3-\sqrt{5}}-\dfrac{1}{3+\sqrt{5}}\right)\) . \(\dfrac{5-\sqrt{5}}{\sqrt{5}-1}\)
2)B = \(\dfrac{1}{1 +\sqrt{2}}\) +\(\dfrac{1}{\sqrt{2}+\sqrt{3}}\)+.....+\(\dfrac{1}{\sqrt{99}+\sqrt{100}}\)
3)C = \(\sqrt[3]{7+5\sqrt{2}}\) - \(\sqrt[3]{7-5\sqrt{2}}\)
4) D = \(\sqrt[3]{9+4\sqrt{5}}\)+\(\sqrt[3]{9-4\sqrt{3}}\)
tính
\(\sqrt{9-4\sqrt{5}}+\sqrt{9+4\sqrt{5}}\)
Bài 1: rút gọn
I=\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
K=\(\sqrt{94-42\sqrt{5}}-\sqrt{94+42\sqrt{5}}\)
Bài 2: tính
Y=\(2+\sqrt{17-4\sqrt{9+4\sqrt{5}}}\)
Z=\(\sqrt[3]{7+5\sqrt{2}}+\sqrt[3]{7-5\sqrt{2}}\)
T=\(\sqrt{3-\sqrt{5}}\left(3+\sqrt{5}\right)\left(\sqrt{10}-\sqrt{2}\right)\)
Giải phương trình:
a) \(x + \sqrt{9 -x^2} = 3 + 5x\sqrt{9 - x^2}\)
b) \(3\sqrt{1 - x^2} = 5\sqrt{1 + x} - 4\sqrt{1 - x} + x + 6\)
c) \(x + 2 + 4\sqrt{x^2 - x + 2} = 2\sqrt{6x^2 - x + 14}\)
Giải PT:
a) -5x+7\(\sqrt{x}\) +12=0
b) \(\dfrac{1}{3}\)\(\sqrt{4x^2-20}\) +2\(\sqrt{\dfrac{x^2-5}{9}}\) -3\(\sqrt{x^2-5}=0\)
c) \(\sqrt{9x+27}+5\sqrt{x+3}-\dfrac{3}{4}\sqrt{16x+48}=5\)
d) \(\sqrt{49x-98}-14\sqrt{\dfrac{x-2}{49}}=3\sqrt{x-2}+8\)
CMR:\(\dfrac{1}{1+\sqrt{3}}+\dfrac{1}{\sqrt{5}+\sqrt{7}}+\dfrac{1}{\sqrt{9}+\sqrt{11}}+...+\dfrac{1}{\sqrt{97}+\sqrt{99}}>\dfrac{9}{4}\)
a,\(\sqrt{x^2-6x+9}=3\) b,\(\sqrt{4x+20}+\sqrt{x+5}-\dfrac{1}{3}\sqrt{9x+45}=4\)
