\(\sqrt{\text{x}}\) = \(\dfrac{\text{5}}{\sqrt{\text{x}}+2}\)
Tìm \(x\)
Giúp e với;-;
K
Khách
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Y
3 tháng 7 2023
\(a,\sqrt{4-2\sqrt{3}}-\sqrt{3}=\sqrt{\sqrt{3^2}-2\sqrt{3}+1}-\sqrt{3}=\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{3}=\left|\sqrt{3}-1\right|-\sqrt{3}=-1\)
\(b,\dfrac{x^2+2\sqrt{2}x+2}{x^2-2}\left(dk:x\ne\pm\sqrt{2}\right)\\ =\dfrac{x^2+2\sqrt{2}x+\sqrt{2^2}}{x^2-\sqrt{2^2}}\\ =\dfrac{\left(x+\sqrt{2}\right)^2}{\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)}\\ =\dfrac{x+\sqrt{2}}{x-\sqrt{2}}\)
\(c,\sqrt{9x^2}-2x\left(dk:x< 0\right)\\ =\sqrt{3^2}.\sqrt{x^2}-2x\\ =3\left|x\right|-2x\\ =-3x-2x\\ =-5x\)
\(d,\sqrt{11+6\sqrt{2}}-3+\sqrt{2}\\ =\sqrt{\sqrt{2^2}+2.3\sqrt{2}+3^2}-3+\sqrt{2}\\ =\sqrt{\left(\sqrt{2}+3\right)^2}-3+\sqrt{2}\\ =\sqrt{2}+3-3+\sqrt{2}\\ =2\sqrt{2}\)
\(e,\dfrac{x^2-5}{x+\sqrt{5}}\left(dk:x\ne-\sqrt{5}\right)\\ =\dfrac{\left(x-\sqrt{5}\right)\left(x+\sqrt{5}\right)}{x+\sqrt{5}}\\ =x-\sqrt{5}\)
KV
5 tháng 6 2023
b) (4√x + 4)/(x + 2√x + 5) ≥ 1
⇔ (4√x + 4)/(x + 2√x + 5) - 1 ≤ 0
Do x ≥ 0 ⇒ x + 2√x + 5 > 0
⇒ (4√x + 4)/(x + 2√x + 5) - 1 ≤ 0
⇔ (4√x + 4) - (x + 2√x + 5) ≤ 0
⇔ 4√x + 4 - x - 2√x - 5 ≤ 0
⇔ -x + 2√x - 1 ≤ 0
⇔ -(x - 2√x + 1) ≤ 0
⇔ -(√x - 1)² ≤ 0 (luôn đúng)
Vậy (4√x + 4)/(x + 2√x + 5) ≤ 1 với mọi x ≥ 0
4 tháng 6 2023
a: \(P=\dfrac{x+8\sqrt{x}+8-x-4\sqrt{x}-4}{\sqrt{x}\left(\sqrt{x}+2\right)}:\dfrac{x+\sqrt{x}+3+\sqrt{x}+2}{\sqrt{x}\left(\sqrt{x}+2\right)}\)
\(=\dfrac{4\left(\sqrt{x}+1\right)}{x+2\sqrt{x}+5}\)
b: 4(căn x+1)>=4
x+2căn x+5>=5
=>P<=4/5<1
ND
Nguyễn Đức Trí
VIP
4 tháng 9 2023
\(P=\dfrac{x^4+5x^3-20x^2-27x+30}{x^2+4x-21}\left(1\right)\)
Điều kiện xác định khi và chỉ khi
\(x^2+4x-21\ne0\)
\(\Leftrightarrow x^2+7x-3x-21\ne0\)
\(\Leftrightarrow x\left(x+7\right)-3\left(x+7\right)\ne0\)
\(\Leftrightarrow\left(x-3\right)\left(x+7\right)\ne0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ne3\\x\ne-7\end{matrix}\right.\)
Theo đề bài : \(\)
\(x=\sqrt[]{31-12\sqrt[]{3}}=\sqrt[]{27-12\sqrt[]{3}+4}=\sqrt[]{\left(3\sqrt[]{3}-2\right)^2}=\left|3\sqrt[]{3}-2\right|=3\sqrt[]{3}-2\)
\(\left(1\right)\Leftrightarrow P=\dfrac{x^4-3x^3+8x^3-24x^2+4x^2-12x-15x+45-15}{\left(x-3\right)\left(x+7\right)}\)
\(\Leftrightarrow P=\dfrac{x^3\left(x-3\right)+8x^2\left(x-3\right)+4x\left(x-3\right)-15\left(x-3\right)-15}{\left(x-3\right)\left(x+7\right)}\)
\(\Leftrightarrow P=\dfrac{\left(x-3\right)\left(x^3+8x^2+4x-15\right)-15}{\left(x-3\right)\left(x+7\right)}\)
\(\Leftrightarrow P=\dfrac{x^3+8x^2+4x-15}{x+7}-\dfrac{15}{\left(x-3\right)\left(x+7\right)}\)
\(\Leftrightarrow P=\dfrac{x^3+7x^2+x^2+7x-3x-15}{x+7}-\dfrac{15}{\left(x-3\right)\left(x+7\right)}\)
\(\Leftrightarrow P=\dfrac{x^2\left(x+7\right)+x\left(x+7\right)-3\left(x+7\right)+6}{x+7}-\dfrac{15}{\left(x-3\right)\left(x+7\right)}\)
\(\Leftrightarrow P=\dfrac{\left(x^2+x-3\right)\left(x+7\right)+6}{x+7}-\dfrac{15}{\left(x-3\right)\left(x+7\right)}\)
\(\Leftrightarrow P=x^2+x-3+\dfrac{6}{x+7}-\dfrac{15}{\left(x-3\right)\left(x+7\right)}\)
Thay \(x=3\sqrt[]{3}-2\) vào \(P\) ta được
\(\Leftrightarrow P=\left(3\sqrt[]{3}-2\right)^2+3\sqrt[]{3}-2-3+\dfrac{6}{3\sqrt[]{3}-2+7}-\dfrac{15}{\left(3\sqrt[]{3}-2-3\right)\left(3\sqrt[]{3}-2+7\right)}\)
\(\Leftrightarrow P=31-12\sqrt[]{3}+3\sqrt[]{3}-5+\dfrac{6}{3\sqrt[]{3}+5}-\dfrac{15}{\left(3\sqrt[]{3}-5\right)\left(3\sqrt[]{3}+5\right)}\)
\(\Leftrightarrow P=26-9\sqrt[]{3}+\dfrac{6\left(3\sqrt[]{3}-5\right)}{\left(3\sqrt[]{3}+5\right)\left(3\sqrt[]{3}-5\right)}-\dfrac{15}{\left(3\sqrt[]{3}\right)^2-5^2}\)
\(\Leftrightarrow P=26-9\sqrt[]{3}+\dfrac{6\left(3\sqrt[]{3}-5\right)}{2}-\dfrac{15}{2}\)
\(\Leftrightarrow P=\dfrac{37}{2}-9\sqrt[]{3}+3\left(3\sqrt[]{3}-5\right)\)
\(\Leftrightarrow P=\dfrac{37}{2}-9\sqrt[]{3}+9\sqrt[]{3}-15\)
\(\Leftrightarrow P=\dfrac{37}{2}-15=\dfrac{7}{2}\)
10 tháng 11 2021
a.\(A=\dfrac{x^2-4x+4}{x^3-2x^2-\left(4x-8\right)}=\dfrac{\left(x-2\right)^2}{x^2\left(x-2\right)-4\left(x-2\right)}=\dfrac{\left(x-2\right)^2}{\left(x^2-4\right)\left(x-2\right)}=\dfrac{x-2}{\left(x-2\right)\left(x+2\right)}=\dfrac{1}{x+2}\)
10 tháng 11 2021
\(A=\dfrac{\left(x-2\right)^2}{x^2\left(x-2\right)-4\left(x-2\right)}\left(x\ne\pm2\right)\\ A=\dfrac{\left(x-2\right)^2}{\left(x-2\right)^2\left(x+2\right)}=\dfrac{1}{x+2}\\ B=\dfrac{x+2-x+\sqrt{x}-1}{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}\cdot\dfrac{4\sqrt{x}}{3}\left(x>0\right)\\ B=\dfrac{4\sqrt{x}\left(\sqrt{x}+1\right)}{3\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}=\dfrac{4\sqrt{x}}{3\left(x-\sqrt{x}+1\right)}\)
7 tháng 3 2022
ĐKXĐ: \(\left\{{}\begin{matrix}x-2>=0\\4-x>=0\\x+1< >0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2< =x< =4\\x< >-1\end{matrix}\right.\Leftrightarrow x\in\left[2;4\right]\)
2 tháng 11 2021
Tham khảo: Bài 4.8 trang 211 Sách bài tập Đại số và giải tích 11: Chứng minh rằng với |x| rất bé so với
2 tháng 11 2021
Tham khảo cách giải:
Đặt \(x\left(y\right)=\sqrt{a^2+x}\) ta có:
\(y'\left(x\right)=\dfrac{\left(a^2+x\right)'}{2\sqrt{a^2+x}}=\dfrac{1}{2\sqrt{a^2+x}}\)
Từ đó:
\(\Delta y=y\left(x\right)-y\left(0\right)\approx y'\left(0\right)x\)
\(\Rightarrow\sqrt{a^2+x}-\sqrt{a^2+0}\approx\dfrac{1}{2\sqrt{a^2+0}}x\)
\(\Rightarrow\sqrt{a^2+x}-a\approx\dfrac{x}{2a}\)
\(\Rightarrow\sqrt{a^2+x}\approx a+\dfrac{x}{2a}\)
Áp dụng :
\(\sqrt{146}=\sqrt{12^2+2}\)
\(\approx12+\dfrac{2}{2.12}\approx12,0833\)
Lời giải:
ĐKXĐ: $x\geq 0$
$\sqrt{x}=\frac{5}{\sqrt{x}+2}$
$\Rightarrow \sqrt{x}(\sqrt{x}+2)=5$
$\Rightarrow x+2\sqrt{x}-5=0$
$\Leftrightarrow (\sqrt{x}+1)^2-6=0$
$\Leftrightarrow (\sqrt{x}+1-\sqrt{6})(\sqrt{x}+1+\sqrt{6})=0$
$\Leftrightarrow \sqrt{x}+1-\sqrt{6}=0$ (do $\sqrt{x}+1+\sqrt{6}>0$)
$\Leftrightarrow \sqrt{x}=\sqrt{6}-1$
$\Leftrightarrow x=7-2\sqrt{6}$ (tm)