Tìm GTLN:C=\(\frac{-7x^2+74x-196}{x^2-10x+25}\)
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L
0
11 tháng 12 2020
a) \(7x\left(x+1\right)-3\left(x+1\right)=0\Rightarrow\left(x+1\right)\left(7x-3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x+1=0\\7x+3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-1\\x=-\dfrac{3}{7}\end{matrix}\right.\)
b) 3(x + 8) - x2 - 8x = 0
=> 3(x + 8) - (x2 + 8x) = 0
=> 3(x + 8) - x(x + 8) = 0
=> (x + 8)(3 - x) = 0 => \(\left[{}\begin{matrix}x+8=0\\3-x=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-8\\x=3\end{matrix}\right.\)
c) \(x^2-10x=-25\Rightarrow x^2-10x+25=0\Rightarrow\left(x-5\right)^2=0\Rightarrow x=5\)
d) Giống câu c
HO
19 tháng 8 2021
a)
b) 3(x + 8) - x2 - 8x = 0
=> 3(x + 8) - (x2 + 8x) = 0
=> 3(x + 8) - x(x + 8) = 0
=> (x + 8)(3 - x) = 0 =>
c)
26 tháng 9 2017
=(-x^2+2xy+2x)-(4y^2-10y+3)
=-(x^2-2xy-2x)-(4y^2-10y+3)
=-[x^2-2x(y-1)]-(4y^2-10y+3)
=-[x^2-2x(y-1)+(y-1)^2]-[4y^2-10y-(y-1)^2+3]
=-[x^2-2x(y-1)+(y-1)^2]-(4y^2-10y-y^2+2y-1+3)
=-(x-y+1)^2-(3y^2-8y+2)
=-(x-y+1)^2-3(y^2-4/3*2*y+16/9+2/3-16/9
=-(x-y+1)^2-3[(y-4/3)^2-10/9]
=-(x-y+1)^2-3(y-4/3)^2+10/3
BN
0
HN
1 tháng 7 2021
a)
⇔ \(x^2-16=9\)
⇔ \(x^2=25\)
⇔ \(x=\pm5\)
b)
⇔ \(x^2-4x+4-25x^2+20x-4=0\)
⇔ \(16x-24x^2=0\)
⇔ \(8x\left(2-3x\right)=0\)
⇒ \(\left[{}\begin{matrix}x=0\\2-3x=0\end{matrix}\right.\) ⇔ \(\left[{}\begin{matrix}x=0\\x=\dfrac{2}{3}\end{matrix}\right.\)
Vậy \(x=0\) hoặc \(x=\dfrac{2}{3}\)
c)
⇔ \(3x^2-10x-20=0\)
⇔ \(x^2-2.x.\dfrac{5}{3}+\dfrac{25}{9}-\dfrac{205}{9}=0\)
⇔ \(\left(x-\dfrac{5}{3}\right)^2=\dfrac{205}{9}\)
⇒ \(\left[{}\begin{matrix}x-\dfrac{5}{3}=\sqrt{\dfrac{205}{9}}\\x-\dfrac{5}{3}=-\sqrt{\dfrac{205}{9}}\end{matrix}\right.\) ⇔ \(\left[{}\begin{matrix}x=\dfrac{\sqrt{\text{205}}}{\text{3}}+\dfrac{5}{3}\\x=-\dfrac{\sqrt{\text{205}}}{\text{3}}+\dfrac{5}{3}\end{matrix}\right.\) ⇔ \(\left[{}\begin{matrix}x=\dfrac{15+\text{9}\sqrt{\text{205}}}{\text{9}}\\\text{x}=-\dfrac{15+\text{9}\sqrt{\text{205}}}{\text{9}}\end{matrix}\right.\)
Vậy...
d)
⇔ \(\left(x^2+x\right)^2-49=\left(x^2+x\right)^2-7x\)
⇔ 7x = 49
⇔ x=7
Vậy...
25 tháng 8 2023
`#040911`
`a)`
`196 - a^2 + 2ab - b^2`
`= 196 - (a^2 - 2ab + b^2)`
`= 196 - (a - b)^2`
`= 14^2 - (a - b)^2`
`= (14 - a + b)(14 + a - b)`
`b)`
`a^2 + 6a - 4b^2 + 9`
`= (a^2 + 6a + 9) - 4b^2`
`= [ (a)^2 + 2*a*3 + 3^2] - (2b)^2`
`= (a + 3)^2 - (2b)^2`
`= (a + 3 - 2b)(a + 3 + 2b)`
`c)`
`4x - 4 + 9y^2 - x^2`
`= 9y^2 - (x^2 - 4x + 4)`
`= (3y)^2 - [ (x)^2 - 2*x*2 + 2^2]`
`= (3y)^2 - (x - 2)^2`
`= (3y - x + 2)(3y + x - 2)`
`d)`
`5x^2 - 10x + 5 - 45t^2`
`= 5*(x^2 - 2x + 1 - 9t^2)`
`= 5*[ (x^2 - 2x + 1) - 9t^2]`
`= 5*{ [(x)^2 - 2*x*1 + 1^2] - (3t)^2}`
`= 5*[ (x - 1)^2 - (3t)^2]`
`= 5*(x - 1 - 3t)(x - 1 + 3t)`
`e)`
`x^2 - 36y^2t^2 - 10x +25`
`= (x^2 - 10x + 25) - 36y^2t^2`
`= [ (x)^2 - 2*x*5 + 5^2] - (6yt)^2`
`= (x - 5)^2 - (6yt)^2`
`= (x - 5 - 6yt)(x - 5 + 6yt)`
25 tháng 8 2023
a: =196-(a^2-2ab+b^2)
=196-(a-b)^2
=(14-a+b)(14+a-b)
b: \(=\left(a^2+6a+9\right)-4b^2\)
\(=\left(a+3\right)^2-4b^2\)
\(=\left(a+3-2b\right)\left(a+3+2b\right)\)
c: \(=9y^2-\left(x^2-4x+4\right)\)
\(=\left(3y\right)^2-\left(x-2\right)^2\)
\(=\left(3y-x+2\right)\left(3y+x-2\right)\)
d: \(=5\left(x^2-2x+1-9t^2\right)\)
\(=5\left[\left(x-1\right)^2-\left(3t\right)^2\right]\)
\(=5\left(x-1-3t\right)\cdot\left(x-1+3t\right)\)
e: \(=x^2-10x+25-36y^2t^2\)
\(=\left(x-5\right)^2-\left(6yt\right)^2\)
\(=\left(x-5-6yt\right)\left(x-5+6yt\right)\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
26 tháng 7 2023
a, 7x + 10x = 5x
17x = 5x
17x - 5x = 0
12x = 0
x =0
2;
a, 4x + 7x = 22
11x = 22
x = 2
b, 12x - 8x = 25
4x = 25
x = \(\dfrac{25}{4}\)
c, \(\dfrac{1}{2}\)x - \(\dfrac{1}{3}\)x = \(\dfrac{4}{5}\)
(\(\dfrac{1}{2}-\dfrac{1}{3}\))x = \(\dfrac{4}{5}\)
\(\dfrac{1}{6}\)x = \(\dfrac{4}{5}\)
x = \(\dfrac{4}{5}\) : \(\dfrac{1}{6}\)
x = \(\dfrac{24}{5}\)
HM
4
30 tháng 8 2021
\(x^2-y^2+7x-7y=\left(x^2-y^2\right)+\left(7x-7y\right)=\left(x-y\right)\left(x+y\right)+7\left(x-y\right)=\left(x-y\right)\left(x+y+7\right)\)
\(x^2-10x+25-9y^2=\left(x^2-10x+25\right)-\left(3y\right)^2=\left(x-5\right)^2-\left(3y\right)^2=\left(x-3y-5\right)\left(x+3y-5\right)\)
30 tháng 8 2021
\(x^2-y^2+7x-7y=\left(x-y\right)\left(x+y\right)+7\left(x-y\right)=\left(x-y\right)\left(x+y+7\right)\)
\(x^2-10x+25-9y^2=\left(x-5\right)^2-\left(3y\right)^2=\left(x-5-3y\right)\left(x-5+3y\right)\)