9 cách

9 cách

a)x=1,414213562

b)x=1,732050808

c)x=1.870828693

d)x=2.029778313

x = 1,414213562

x = 1,732050808

x = 1.870828693

x = 2.029778313

a/ \(\sqrt{17}+\sqrt{5}+1>\sqrt{16}+\sqrt{4}+1=4+2+1=7\)

\(\sqrt{45}< \sqrt{49}=7\)

\(\Rightarrow\sqrt{17}+\sqrt{5}+1>\sqrt{45}\)

b/ Ta có:

\(\sqrt{n}< \sqrt{n+1}\)

\(\Rightarrow2\sqrt{n}< \sqrt{n+1}+\sqrt{n}\)

\(\Rightarrow\dfrac{1}{\sqrt{n}}>\dfrac{2}{\sqrt{n+1}+\sqrt{n}}=2\left(\sqrt{n+1}-\sqrt{n}\right)\)

Áp dụng vào bài toán được

\(1+\dfrac{1}{\sqrt{2}}+\dfrac{1}{\sqrt{3}}+...+\dfrac{1}{\sqrt{36}}>2\left(\sqrt{2}-\sqrt{1}+\sqrt{3}-\sqrt{2}+...+\sqrt{37}-\sqrt{36}\right)\)

\(=2\left(\sqrt{37}-1\right)>6\)

\(\left(a^3+b^3\right)\left(a^2+b^2\right)-\left(a+b\right)=a^5+a^3b^2+a^2b^3+b^5-\left(a+b\right)\)

                                                                =  \(a^5+b^5+a^2b^2\left(a+b\right)-\left(a+b\right)\)

                                                                =\(a^5+b^5+\left(a+b\right)-\left(a+b\right)\)

                                                               =\(a^5+b^5\left(dpcm\right)\)

\(\sqrt{156^2-124^2}\)

Áp dụng hằng đẳng thức \(A^2-B^2=\left(A-B\right)\left(A+B\right)\)

Ta được

\(\sqrt{156^2-124^2}\)

\(=\sqrt{\left(156-124\right)\left(156+124\right)}\)

\(=\sqrt{32\times280}\)

\(=16\sqrt{35}\)

Ok