\(x^3=10+3x\sqrt[3]{\left(5-\sqrt{17}\right)\left(5+\sqrt{17}\right)}=10+6x\)

Thay vào -> dpcm

\(x=\sqrt[3]{5-\sqrt{17}}+\sqrt[3]{5+\sqrt{17}}\)

\(\Leftrightarrow x^3=5-\sqrt{17}+5+\sqrt{17}\)

\(+3\left(\sqrt[3]{5-\sqrt{17}}+\sqrt[3]{5+\sqrt{17}}\right)\sqrt[3]{5-\sqrt{17}}\sqrt[3]{5+\sqrt{17}}\)

\(\Leftrightarrow x^3=10+3x\sqrt[3]{\left(5-\sqrt{17}\right)\left(5+\sqrt{17}\right)}\)

\(\Leftrightarrow x^3=10+3x\sqrt[3]{8}\Leftrightarrow x^3=10+6x\)

\(\Leftrightarrow x^3-6x-10=0\)

\(\Rightarrow\) Đpcm

Chúc bạn học tốt !!!

\(x=\sqrt[3]{5-\sqrt{17}}+\sqrt[3]{5+\sqrt{17}}\)

\(\Leftrightarrow x^3=5-\sqrt{17}+5+\sqrt{17}+3\left(\sqrt[3]{5-\sqrt{17}}+\sqrt[3]{5+\sqrt{17}}\right)\sqrt[3]{5-\sqrt{17}}\sqrt[3]{5+\sqrt{17}}\)

\(\Leftrightarrow x^3=10+3x\sqrt[3]{\left(5-\sqrt{17}\right)\left(5+\sqrt{17}\right)}\)

\(\Leftrightarrow x^3=10+3x\sqrt[3]{8}\)\(\Leftrightarrow x^3=10+6x\)

\(\Leftrightarrow x^3-6x-10=0\)

Hay ta co DPCM

\(x=\sqrt[3]{5-\sqrt{17}}+\sqrt[3]{5+\sqrt{17}}\)

\(\Rightarrow x^3=5-\sqrt{17}+5+\sqrt{17}+3\sqrt[3]{\left(5-\sqrt{17}\right)\left(5+\sqrt{17}\right)}x\)

\(\Rightarrow x^3=10+3\sqrt[3]{25-17}x\)

\(\Rightarrow x^3=10+3\sqrt[3]{8}x\)

\(\Rightarrow x^3=10+3.2x\)

\(\Leftrightarrow x^3-6x-10=0\)

Học toán vui vẻ!

a: Ta có: \(\sqrt{4x+20}-3\sqrt{x+5}+\dfrac{4}{3}\sqrt{9x+45}=6\)

\(\Leftrightarrow2\sqrt{x+5}-3\sqrt{x+5}+4\sqrt{x+5}=6\)

\(\Leftrightarrow3\sqrt{x+5}=6\)

\(\Leftrightarrow x+5=4\)

hay x=-1

b: Ta có: \(\dfrac{1}{2}\sqrt{x-1}-\dfrac{3}{2}\sqrt{9x-9}+24\sqrt{\dfrac{x-1}{64}}=-17\)

\(\Leftrightarrow\dfrac{1}{2}\sqrt{x-1}-\dfrac{9}{2}\sqrt{x-1}+3\sqrt{x-1}=-17\)

\(\Leftrightarrow\sqrt{x-1}=17\)

\(\Leftrightarrow x-1=289\)

hay x=290

\(x^3=76+3\sqrt[3]{\left(38-17\sqrt{5}\right)\left(38+17\sqrt{5}\right)}\left(\sqrt[3]{38-17\sqrt{5}}+\sqrt[3]{38+17\sqrt{5}}\right)\)

\(\Leftrightarrow x^3=76-3x\)

\(\Leftrightarrow x^3+3x-76=0\)

\(\Leftrightarrow\left(x-4\right)\left(x^2+4x+19\right)=0\)

\(\Leftrightarrow x=4\)

\(\Rightarrow x^3-3x^2-2x-8=0\)

đố anh làm được đấy

Đáp án :

\(x_0=^3\sqrt{38-17}\sqrt{5}+^3\sqrt{38+17}.\sqrt{5}\)

\(=x_0=38-17\sqrt{5}+38+17\sqrt{5}-3^3\sqrt{\left(38-17\sqrt{5}\right)\left(38+17\sqrt{5}\right).x_0}\)

\(=76-3^3\sqrt{-1}.x_0=76+3x_0\)

\(=x_0^3\)\(-3x_0-76=0\)

\(=\left(x_0-4\right)\left(x_0^2+4x_0+19\right)=0\)

\(=x_0=4\)

Thay x0 = 4 vào phương trình x3 - 3x2 - 2x - 8 = 0 ta có đẳng thức đúng là:

    43 - 3.42 - 2.4 - 8 = 0

    Vậy x0 là nghiệm của phương trình x3 - 3x2 - 2x - 8 = 0

biết mà vẫn hỏi

a: ĐKXĐ: x>=-3/2

\(\sqrt{x^2+4}=\sqrt{2x+3}\)

=>\(x^2+4=2x+3\)

=>\(x^2-2x+1=0\)

=>\(\left(x-1\right)^2=0\)

=>x-1=0

=>x=1(nhận)

b: \(\sqrt{x^2-6x+9}=2x-1\)(ĐKXĐ: \(x\in R\))

=>\(\sqrt{\left(x-3\right)^2}=2x-1\)

=>\(\left\{{}\begin{matrix}\left(2x-1\right)^2=\left(x-3\right)^2\\x>=\dfrac{1}{2}\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}\left(2x-1-x+3\right)\left(2x-1+x-3\right)=0\\x>=\dfrac{1}{2}\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}\left(x+2\right)\left(3x-4\right)=0\\x>=\dfrac{1}{2}\end{matrix}\right.\)

=>x=4/3(nhận) hoặc x=-2(loại)

c:

Sửa đề: \(\sqrt{4x+12}=\sqrt{9x+27}-5\)

ĐKXĐ: \(x>=-3\)

\(\sqrt{4x+12}=\sqrt{9x+27}-5\)

=>\(2\sqrt{x+3}=3\sqrt{x+3}-5\)

=>\(-\sqrt{x+3}=-5\)

=>x+3=25

=>x=22(nhận)

d: ĐKXĐ: \(\left[{}\begin{matrix}x< =\dfrac{3-\sqrt{5}}{4}\\x>=\dfrac{3+\sqrt{5}}{4}\end{matrix}\right.\)
\(\sqrt{4x^2-6x+1}=\left|2x-5\right|\)

=>\(\sqrt{\left(4x^2-6x+1\right)}=\sqrt{4x^2-20x+25}\)

=>\(4x^2-6x+1=4x^2-20x+25\)

=>\(-6x+20x=25-1\)

=>\(14x=24\)

=>x=12/7(nhận)