a) \(M=\sqrt[3]{7+5\sqrt{2}}\)

Ta có:

Vì \(7+5\sqrt{2}=\left(\sqrt{2}\right)^3+1+3\sqrt{2}.1\left(\sqrt{2}+1\right)=\left(\sqrt{2}+1\right)^3\)

Nên \(M=\sqrt[3]{\left(\sqrt{2}+1\right)^3}=\sqrt{2}+1\)

b) \(N=\sqrt[3]{6\sqrt{3}-10}\)

Ta có:

Vì \(6\sqrt{3}-10=\left(\sqrt{3}\right)^3-1^3-3\sqrt{3}.1\left(\sqrt{3}-1\right)=\left(\sqrt{3}-1\right)^3\)

Nên \(N=\sqrt[3]{\left(\sqrt{3}-1\right)^3=\sqrt{3}-1}\)

xem gi

co ban nho cua toi       

may bi loi unikey thong cam nha moi nguoi

hihi

a) \(\sqrt[3]{x}< 2\Leftrightarrow\left(\sqrt[3]{x}\right)^3< 2^3\Leftrightarrow x< 8\)

b) \(\sqrt[3]{2x-1}>-3\Leftrightarrow\left(\sqrt[3]{2x-1}\right)^3>\left(-3\right)^3\Leftrightarrow2x-1>-27\Leftrightarrow2x>-26\Leftrightarrow x>-13\)

c) \(\sqrt[3]{2-3x}\le1\Leftrightarrow\left(\sqrt[3]{2-3x}\right)^3\le1\Leftrightarrow2-3x\le1\Leftrightarrow3x\ge1\Leftrightarrow x\ge\frac{1}{3}\)

d) \(\sqrt[3]{3-4x}\ge5\Leftrightarrow\left(\sqrt[3]{3-4x}\right)^3\ge5^3\Leftrightarrow3-4x\ge125\Leftrightarrow4x\le-122\Leftrightarrow x\le-\frac{61}{2}\)

a) \(\hept{\begin{cases}\left(x+1\right)\left(y+1\right)=8\\x\left(x+1\right)+y\left(y+1\right)+xy=17\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x+y+xy=7\\x^2+y^2+x+y+xy=17\end{cases}}\)

Dat \(\hept{\begin{cases}xy=P\\x+y=S\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}S+P=7\\S^2+S-P=17\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}P=7-S\\S^2+S-\left(7-S\right)=17\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}P=7-S\\S^2+2S=24\end{cases}}\)

\(\hept{\begin{cases}S=-6\\P=13\\S=4;P=3\end{cases}}\)

b) 

a) $x^3=2\iff x=\sqrt[3]{2}$.

b) $27x^3=-81\iff x^3=-3\iff \sqrt[3]{x^3}=\sqrt[3]{-3}\iff x=-\sqrt[3]{3}$.

c) $\genfrac{}{}{0ex}{}{1}{2}{x}^3=0,004\iff x^3=0,008\iff \sqrt[3]{x^3}=\sqrt[3]{0,008}\iff x=0,2.$

d) $\sqrt[3]{3x+1}=4\iff 3x+1=4^3\iff x=21.$

e) $\sqrt[3]{3-2x}=-3\iff 3-2x=(-3{)}^3\iff x=15.$

f) $\sqrt[3]{x-2}+2=x\iff \sqrt[3]{x-2}=x-2\iff x-2=(x-2{)}^3.$

$\iff (x-2)\left[(x-2{)}^2-1\right]=0\iff [\begin{array}{l}x-2=1\\ (x-2{)}^2=1\end{array}\iff [\begin{array}{l}x=2\\ x-2=1\\ x-2=-1\end{array}\iff [\begin{array}{l}x=2\\ x=3\\ x=1\end{array}.$

a) x=\(\sqrt[3]{2}\)         b x=\(\sqrt[3]{-3}\)     c) x=0,2       d)x=21       e) x=15      f) x=3

Sẽ có đáp án

copi mậng được ko hả anh 

30,001x3​=3(0,1x)3​=0,1x;

\sqrt[3]{-125 a^{12}}=\sqrt[3]{\left(-5 a^{4}\right)^{3}}=-5 a^{4};3−125a12​=3(−5a4)3​=−5a4;

\sqrt[3]{27 x^{6}}=\sqrt[3]{\left(3 x^{2}\right)^{3}}=3 x^{2};327x6​=3(3x2)3​=3x2;

\sqrt[3]{-0,343 a^{3}}=\sqrt[3]{(-0,7 a)^{3}}=-0,7 a;3−0,343a3​=3(−0,7a)3​=−0,7a;

Ta rút gọn các biểu thức như sau:

\(\sqrt[3]{0,001x^3}=\sqrt[3]{\left(0,1x\right)^3}=0,1x.\)

\(\sqrt[3]{-125a^{12}}=\sqrt[3]{\left(-5a^4\right)^3}=-5a^4\)

\(\sqrt[3]{27x^6}=\sqrt[3]{\left(3x^2\right)^3}=3x^2\)

\(\sqrt[3]{-0,343a^3}=\sqrt[3]{\left(-0,7a\right)^3}=-0,7a\)

\(\sqrt{x}+\sqrt{x+1}=\frac{1}{\sqrt{x}}\)

\(\Rightarrow\sqrt{x}\sqrt{x}+\sqrt{x+1}\sqrt{x}=\frac{1}{\sqrt{x}}\sqrt{x}\)

\(\Rightarrow\left(\sqrt{x}\right)^2+\sqrt{x}\sqrt{x+1}=1\)

\(\Rightarrow x^2+x=1-2x+x^2\)

\(\Rightarrow x=1-2x\)

\(\Rightarrow3x=1\)

\(\Rightarrow x=\frac{1}{3}\)

\(\Rightarrow S=\frac{1}{3}\)

Vậy nghiệm phương trình là \(\frac{1}{3}\)

1 = 1 = 2