the maximum value of \(\frac{\left(x^2+15\right)}{x^2+3}\)
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Find the maximum and minimum value of the expression
\(\frac{x+y+z}{3}+\frac{2016}{\sqrt[3]{xyz}}\)if \(x,y,z\in\left[1,2016\right]\)
Đặt \(A=\frac{x+y+z}{3}+\frac{2016}{\sqrt[3]{xyz}}\)
Tìm giá trị nhỏ nhất :Áp dụng bđt Cauchy : \(A=\frac{x+y+z}{3}+\frac{2016}{\sqrt[3]{xyz}}\ge\frac{3.\sqrt[3]{xyz}}{3}+\frac{2016}{\sqrt[3]{xyz}}\)
\(\Rightarrow A\ge\sqrt[3]{xyz}+\frac{2016}{\sqrt[3]{xyz}}\ge2\sqrt{\sqrt[3]{xyz}.\frac{2016}{\sqrt[3]{xyz}}}\)
\(\Rightarrow A\ge2\sqrt{2016}=24\sqrt{14}\) .
Dấu "=" xảy ra khi và chỉ khi \(\begin{cases}x=y=z\\\sqrt[3]{xyz}=\frac{2016}{\sqrt[3]{xyz}}\end{cases}\) \(\Leftrightarrow x=y=z=12\sqrt{14}\)
Vậy A đạt giá trị nhỏ nhất bằng \(24\sqrt{14}\) tại \(x=y=z=12\sqrt{14}\)
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Find the value of the remainder of the division
\(\left(7x-2x^3+4x^4-5\right):\left(x^2+2\right)\)with \(x=\frac{-1}{11}\)
Answer: The value of the remainder is ....
Nhah nha đag cần gấp
let P(x) be a polynomial of degree 3 and x1, x2, x3 are the solutions of P(x)=0. let \(\frac{P\left(\frac{1}{3}\right)-P\left(\frac{-1}{3}\right)}{P\left(0\right)}=8,\frac{P\left(\frac{1}{4}\right)-P\left(\frac{-1}{4}\right)}{P\left(0\right)}=9\)and x1+x2+x3 = 35. find the value of \(\frac{x2+x3}{x1}+\frac{x1+x3}{x2}+\frac{x1+x2}{x3}\)
Find the value of x such that: \(\frac{3\left(x+2\right)}{2x+3}=\frac{7}{8},\left(x\ne-\frac{3}{2}\right)\) . Answer: x = ...
( write your answer by decimal in simplest form )
The value of such that \(3.\left(\frac{1}{7}-\frac{3}{21}+\frac{7}{3}\right)<\frac{x}{2}<\frac{13}{8}.\left(\frac{1}{2}-\frac{1}{6}\right)\)
Answer: x =
a) The minimum value of \(\sqrt{5x-1}+\left(1.1\right)^2\)
b) The maximum value of \(1.21-\sqrt{11-3x}\)
a) Ta có :
\(\sqrt{5X-1}\ge0\) => \(\sqrt{5X-1}+\left(1,1\right)^2\ge\left(1,1\right)^2\) Vậy GTNN là 1,21
b) Ta có
\(\sqrt{11-3X}\ge0\) =>\(-\sqrt{11-3X}\le0\) =>\(1,21-\sqrt{11-3X}\le1,21\) GTLN là 1,21
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kết quả câu a) ko phải là 1 ; kết quả câu b) ko phải là 21
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Xem thêm câu trả lời
the maximum value of C=x2+8/(2(x2+2)
given 1<x<3., Find the value of \(A=\frac{\left|x-3\right|}{x-3}-\frac{\left|x-1\right|}{1-x} +\left|x-1\right|+\left|3-x\right|\)
Answer:A=...........
Lời giải:
Vì \(1< x< 3\Rightarrow \left\{\begin{matrix}
|x-3|=|3-x|=3-x\\
|x-1|=x-1\end{matrix}\right.\). Khi đó:
\(A=\frac{|x-3|}{x-3}-\frac{|x-1|}{1-x}+|x-1|+|3-x|\)
\(=\frac{3-x}{x-3}-\frac{x-1}{1-x}+x-1+3-x\)
\(=-1-(-1)+2=2\)
Vậy giá trị của $A$ là $2$
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Question 1:Fill the suitable number in the following blank?.343_____3Question 2:The positive value of such that left|2x-3right|+716 is _______Question 3:Given a function gleft(xright)2sqrt{x-7} . Find the value of gleft(11right)?Answer: The value of gleft(11right) is ._________Question 4:Find the value of such that 0,008left(0,2right)^x.Answer: . x_________Question 5:Given a functiongleft(xright)frac{2}{3-x} . Find the value of .gleft(1right)+gleft(2right)Answer: The value of gleft(1right)+gl...
Đọc tiếp
Question 1:
Fill the suitable number in the following blank?
.\(343=\)_____\(3\)
Question 2:
The positive value of such that \(\left|2x-3\right|+7=16\) is _______
Question 3:
Given a function \(g\left(x\right)=2\sqrt{x-7}\) . Find the value of \(g\left(11\right)\)?
Answer: The value of \(g\left(11\right)\) is ._________
Question 4:
Find the value of such that \(0,008=\left(0,2\right)^x\).
Answer: . \(x=\)_________
Question 5:
Given a function\(g\left(x\right)=\frac{2}{3-x}\) . Find the value of .\(g\left(1\right)+g\left(2\right)\)
Answer: The value of \(g\left(1\right)+g\left(2\right)\) is ._______
Question 6:
Suppose that \(\frac{7y-x}{2x+y}=\frac{1}{3}\) then the ratio of \(x\) to \(y\) is .________
Question 7:
If \(x\) is directly proportional to \(y\) with the scaling factor is 8, \(z\) is directly proportional to \(x\) with the scaling factor is 4.
Then \(z\) is directly proportional to \(y\) with the scaling factor is______ .
Question 8:
The maximum value of \(A=\frac{6}{2.\left(x-3\right)^2+3}\) is .______
Question 10:
Suppose that\(\frac{7-3x}{5}=\frac{y+4}{3}=\frac{6x-y}{5}\) . Find the ratio of \(y\) to \(x\)
Answer: The ratio of \(y\) to \(x\) is .______________-
(write your answer by decimal in simplest form)
you may also be investigated google it.
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1 là 34 5 là 3 10 là ?
2 là 6 6 là 1/4
3 là 4 7 là 32
4 là 3 8 là 2
good luck!
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