(7x+2)2−(7x−5)2
Tìm x để các phân số sau tối giản:
7x+1 /2, 7x+2 /3, 7x+3 /4, 7x+4 /5, ....., 7x+300 /301
do các phân số ở hàng số thứ 2 đã tối giản nên x=0=>7x=0 =>tổng các phân số sau đều tối giản
(7x-5)^2-4x^2(7x-5)=0
(7x-5)2-4x2(7x-5)=0
<=>(7x-5)(7x-5-4x2)=0
<=>7x-5=0 hoặc 7x-5-4x2=0
<=>x=5/7 (vì \(\Delta_{7x-55-4x^2}=\left(-7\right)^2-4\left(4\cdot5\right)=-31< 0\)(vn))
Vậy x=5/7
Δ7x−55−4x2=(−7)2−4(4·5)=−31<0(vn)) cái dòng này mình ko hỉu
Tính giá trị biểu thức:
A = \(7x^7-7x^6+7x^5-7x^4+7x^3-7x^2+7x-100\)
tìm giá trị lớn nhất của biểu thức A = 2(7x+5)^2+11/(7x+5)^2+4
\(A=\dfrac{2\left(7x+5\right)^2+11}{\left(7x+5\right)^2+4}\)
\(\Rightarrow A=\dfrac{2\left(7x+5\right)^2+8+3}{\left(7x+5\right)^2+4}\)
\(\Rightarrow A=\dfrac{2\left[\left(7x+5\right)^2+4\right]+3}{\left(7x+5\right)^2+4}\)
\(\Rightarrow A=2+\dfrac{3}{\left(7x+5\right)^2+4}\left(1\right)\)
Ta lại có :
\(\left(7x+5\right)^2\ge0,\forall x\in R\)
\(\Rightarrow\left(7x+5\right)^2+4\ge4,\forall x\in R\)
\(\Rightarrow\dfrac{1}{\left(7x+5\right)^2+4}\le\dfrac{1}{4},\forall x\in R\)
\(\Rightarrow\dfrac{3}{\left(7x+5\right)^2+4}\le\dfrac{3}{4},\forall x\in R\)
\(\left(1\right)\Rightarrow A=2+\dfrac{3}{\left(7x+5\right)^2+4}\le2+\dfrac{3}{4}=\dfrac{11}{4},\forall x\in R\)
Dấu "=" xảy ra khi và chỉ khi
\(7x+5=0\)
\(\Rightarrow x=-\dfrac{5}{7}\)
Vậy \(GTLN\left(A\right)=\dfrac{11}{4}\left(khi.x=-\dfrac{5}{7}\right)\)
giải phương trình
\(7x^8+7x^7+7x^6+7x^5+7x^4+4x^3+4x^2+4x+9\)
( 7x-5)-(x-2)*(7x-5)
x^2 + 6x + 5
x^2 - 7x + 12
x^2 -7x + 10
\(x^2+6x+5=x^2+5x+x+5=x\left(x+5\right)+\left(x+5\right)=\left(x+1\right)\left(x+5\right)\)
\(x^2-7x+12=x^2-4x-3x+12=x\left(x-4\right)-3\left(x-4\right)=\left(x-3\right)\left(x-4\right)\)
\(x^2-7x+10=x^2-2x-5x+10=x\left(x-2\right)-5\left(x-2\right)=\left(x-2\right)\left(x-5\right)\)
\(a,x^2+6x+5=x^2+5x+x+5\)
\(=x\left(x+5\right)+\left(x+5\right)=\left(x+5\right)\left(x+1\right)\)
\(b,\)\(x^2-7x+12=x^2-3x-4x+12\)
\(=x\left(x-3\right)-4\left(x-3\right)=\left(x-3\right)\left(x-4\right)\)
\(c,\)\(x^2-7x+10=x^2-2x-5x+10\)
\(=x\left(x-2\right)-5\left(x-2\right)=\left(x-2\right)\left(x-5\right)\)
a) \(x^2+6x+5=x^2+5x+x+5\)
\(=x\left(x+5\right)+\left(x+5\right)=\left(x+1\right)\left(x+5\right)\)
b)\(x^2-7x+12=x^2-4x-3x+12=x\left(x-4\right)-3\left(x-4\right)=\left(x-3\right)\left(x-4\right)\)
c)\(x^2-7x+10=x^2-2x-5x+10=x\left(x-2\right)-5\left(x-2\right)\)
\(=\left(x-5\right)\left(x-2\right)\)
hc tốt
Tìm đa thức A biết :
1. A + 7x mũ 2 × y - 5 xy mũ 2 - xy = x mũ 2× y + 8 xy mũ 2 - 5 xy
2. 4 xy mũ 2 - 7x + 1 - A = 3x mũ 2 - 7x - 1
1. \(A+7x^2y-5xy^2-xy=x^2y+8xy^2-5xy\)
\(\Rightarrow A+7x^2y-x^2y-5xy^2-8xy^2-xy+5xy=0\)
\(\Rightarrow A+6x^2y-13xy^2+4xy=0\)
\(\Rightarrow A=-6x^2y+13xy^2-4xy\)
2. \(4xy^2-7x+1-A=3x^2-7x-1\)
\(\Rightarrow4xy^2-3x^2-7x+7x+1+1-A=0\)
\(\Rightarrow4xy^2-3x^2+2-A=0\)
\(\Rightarrow A=4xy^2-3x^2+2\)
Tìm x,biết:
a) x^2 - 4x -5 = 0
b) 4x^2 + 7x - 11 = 0
c) -7x^2 + 6x + 1 = 0
d) - 10x^2 +7x+3 = 0
a) x2 - 4x - 5 = 0
=> x2 - 5x + x - 5 = 0
=> x(x - 5) + (x - 5) = 0
=> (x + 1)(x - 5) = 0
=> \(\orbr{\begin{cases}x+1=0\\x-5=0\end{cases}}\)
=> \(\orbr{\begin{cases}x=-1\\x=5\end{cases}}\)
b) 4x2 + 7x - 11 = 0
=> 4x2 + 11x - 4x - 11 = 0
=> x(4x + 11) - (4x + 11) = 0
=> (x - 1)(4x + 11) = 0
=> \(\orbr{\begin{cases}x-1=0\\4x+11=0\end{cases}}\)
=> \(\orbr{\begin{cases}x=1\\x=-\frac{11}{4}\end{cases}}\)
c) -7x2 + 6x + 1 = 0
=> -7x2 + 7x - x + 1 = 0
=> -7x(x - 1) - (x - 1) = 0
=> (-7x - 1)(x - 1) = 0
=> \(\orbr{\begin{cases}-7x-1=0\\x-1=0\end{cases}}\)
=> \(\orbr{\begin{cases}-7x=1\\x=1\end{cases}}\)
=> \(\orbr{\begin{cases}x=-\frac{1}{7}\\x=1\end{cases}}\)
d) -10x2 + 7x + 3 = 0
=> -10x2 + 10x - 3x + 3 = 0
=> -10x(x - 1) - 3(x - 1) = 0
=> (-10x - 3)(x - 1) = 0
=> \(\orbr{\begin{cases}-10x-3=0\\x-1=0\end{cases}}\)
=> \(\orbr{\begin{cases}-10x=3\\x=1\end{cases}}\)
=> \(\orbr{\begin{cases}x=-\frac{3}{10}\\x=1\end{cases}}\)
\(a,x^2-4x-5=0\)
\(\Rightarrow x^2-5x+x-5=0\)
\(\Rightarrow x\left(x-5\right)+\left(x-5\right)=0\)
\(\Rightarrow\left(x-5\right)\left(x+1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-5=0\\x+1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=5\\x=-1\end{cases}}}\)
\(b,4x^2+7x-11=0\)
\(\Rightarrow4x^2-4x+11x-11=0\)
\(\Rightarrow4x\left(x-1\right)+11\left(x-1\right)=0\)
\(\Rightarrow\left(x-1\right)\left(4x+11\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-1=0\\4x+11=0\end{cases}\Rightarrow\orbr{\begin{cases}x=1\\x=-\frac{11}{4}\end{cases}}}\)
\(c,-7x^2+6x+1=0\)
\(\Rightarrow-7x^2+7x-x+1=0\)
\(\Rightarrow-7x\left(x-1\right)-\left(x-1\right)=0\)
\(\Rightarrow\left(x-1\right)\left(-7x-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-1=0\\-7x-1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=1\\x=-\frac{1}{7}\end{cases}}}\)
\(d,-10x^2+7x+3=0\)
\(\Rightarrow-10x^2+10x-3x+3=0\)
\(\Rightarrow-10x\left(x+1\right)-3\left(x+1\right)=0\)
\(\Rightarrow\left(x+1\right)\left(-10x-3\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x+1=0\\-10x-3=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-1\\x=-\frac{3}{10}\end{cases}}}\)