Giups mình với ạ. Cảm ơn mng nhiều
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\(a,A=0,2\left(5x-1\right)-\dfrac{1}{2}\left(\dfrac{2}{3}x+4\right)+\dfrac{2}{3}\left(3-x\right)\)
\(=x-0,2-\dfrac{1}{3}x-2+2-\dfrac{2}{3}x\)
\(=\left(-0,2-2+2\right)+\left(x-\dfrac{1}{3}x-\dfrac{2}{3}x\right)\)
\(=-0,2\)
\(b,B=\left(x-2y\right)\left(x^2+2xy+4y^2\right)-\left(x^3-8y^3+10\right)\)
\(=x^3-8y^3-x^3+8y^3-10\)
\(=-10\)
\(c,C=4\left(x+1\right)^2+\left(2x-1\right)^2-8\left(x-1\right)\left(x+1\right)-4x\)
\(=4\left(x^2+2x+1\right)+\left(4x^2-4x+1\right)-8\left(x^2-1\right)-4x\)
\(=4x^2+8x+4+4x^2-4x+1-8x^2+8-4x\)
\(=13\)
a) \(A=0,2\left(5x-1\right)-\dfrac{1}{2}\left(\dfrac{2}{3}x+4\right)+\dfrac{2}{3}\left(3-x\right)\)
\(A=x-\dfrac{1}{5}-\dfrac{1}{3}x-2+2-\dfrac{2}{3}x\)
\(A=\left(x-\dfrac{1}{3}x-\dfrac{2}{3}x\right)-\left(\dfrac{1}{5}+2-2\right)\)
\(A=-\dfrac{1}{5}\)
Vậy: ...
b) \(B=\left(x-2y\right)\left(x^2+2xy+4y^2\right)-\left(x^3-8y^3+10\right)\)
\(B=\left[x^3-\left(2y\right)^3\right]-\left[x^3-\left(2y\right)^3\right]-10\)
\(B=-10\)
Vậy: ...
c) \(4\left(x+1\right)^2+\left(2x-1\right)^2-8\left(x+1\right)\left(x-1\right)-4x\)
\(=4\left(x^2+2x+4\right)+\left(4x^2-4x+1\right)-8\left(x^2-1\right)-4x\)
\(=4x^2+8x+4+4x^2-4x+1-8x^2+8-4x\)
\(=\left(4x^2+4x^2-8x^2\right)+\left(8x-4x-4x\right)+\left(4+1+8\right)\)
\(=13\)
Vậy:...
e: \(=\left|3-\sqrt{2}\right|=3-\sqrt{2}\)
h: \(=3-\sqrt{2}+3+\sqrt{2}=6\)
g: \(=\left|0.1-\sqrt{0.1}\right|=0.1-\sqrt{0.1}\)
i: \(=\left|2\sqrt{2}-3\right|=3-2\sqrt{2}\)
c: \(=\left|2+5\right|=7\)
o: \(=5-2\sqrt{6}-5-2\sqrt{6}=-4\sqrt{6}\)
n: \(=4-2\sqrt{3}+4+2\sqrt{3}=8\)
m: \(=7+2\sqrt{10}-7-2\sqrt{10}=0\)
Bài 2:
a: \(f\left(x\right)=-9x^3-2x^2+6x-3\)
\(G\left(x\right)=9x^3-6x+53\)
b: \(H\left(x\right)=9x^3-6x+53-9x^3-2x^2+6x-3=-2x^2+50\)
c: Đặt H(x)=0
=>2x2-50=0
=>x=5 hoặc x=-5
\(\left(7\dfrac{4}{9}+4\dfrac{7}{11}\right)-3\dfrac{4}{9}\)
\(=\dfrac{67}{9}+\dfrac{51}{11}-\dfrac{31}{9}\)
\(=\dfrac{67}{9}-\dfrac{31}{9}+\dfrac{51}{11}\)
\(=4+\dfrac{51}{11}\)
\(=\dfrac{95}{11}\)
Chúc bạn học tốt
Lời giải:
ĐK: $x>0; x\neq 1$
a.
\(P=\frac{3}{\sqrt{x}}+\left[\frac{x}{\sqrt{x}(\sqrt{x}-1)}+\frac{x+1}{\sqrt{x}}-\frac{1}{\sqrt{x}-1}\right].\frac{\sqrt{x}}{x+\sqrt{x}+1}\)
\(=\frac{3}{\sqrt{x}}+\left[\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{1}{\sqrt{x}-1}+\frac{x+1}{\sqrt{x}}\right].\frac{\sqrt{x}}{x+\sqrt{x}+1}\)
\(=\frac{3}{\sqrt{x}}+\left[\frac{\sqrt{x}-1}{\sqrt{x}-1}+\frac{x+1}{\sqrt{x}}\right].\frac{\sqrt{x}}{x+\sqrt{x}+1}\)
\(=\frac{3}{\sqrt{x}}+(1+\frac{x+1}{\sqrt{x}}).\frac{\sqrt{x}}{x+\sqrt{x}+1}=\frac{3}{\sqrt{x}}+\frac{x+\sqrt{x}+1}{\sqrt{x}}.\frac{\sqrt{x}}{x+\sqrt{x}+1}=\frac{3}{\sqrt{x}}+1\)
b.
$P\geq 10\Leftrightarrow \frac{3}{\sqrt{x}}+1\geq 10$
$\Leftrightarrow \frac{3}{\sqrt{x}}\geq 9$
$\Leftrightarrow \sqrt{x}\leq \frac{1}{3}$
$\Leftrightarrow x\leq \frac{1}{9}$
Kết hợp với ĐKXĐ suy ra $0< x\leq \frac{1}{9}$
c.
Để $P$ nguyên thì $\frac{3}{\sqrt{x}}$ nguyên.
Với $x$ nguyên, điều này xảy ra khi $\sqrt{x}$ là ước của $3$
$\Leftrightarrow \sqrt{x}\in\left\{1; 3\right\}$
$\Leftrightarrow x\in\left\{1; 9\right\}$
Vì $x\neq 1$ nên $x=9$