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LA
1
11 tháng 8 2023
a) \(4x^2+16x+3=0\)
\(\Delta'=84-12=72\Rightarrow\sqrt[]{\Delta'}=6\sqrt[]{2}\)
Phương trình có 2 nghiệm
\(\left[{}\begin{matrix}x=\dfrac{-8+6\sqrt[]{2}}{4}\\x=\dfrac{-8-6\sqrt[]{2}}{4}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-2\left(4-3\sqrt[]{2}\right)}{4}\\x=\dfrac{-2\left(4+3\sqrt[]{2}\right)}{4}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-\left(4-3\sqrt[]{2}\right)}{2}\\x=\dfrac{-\left(4+3\sqrt[]{2}\right)}{2}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3\sqrt[]{2}-4}{2}\\x=\dfrac{-3\sqrt[]{2}-4}{2}\end{matrix}\right.\)
b) \(7x^2+16x+2=1+3x^2\)
\(4x^2+16x+1=0\)
\(\Delta'=84-4=80\Rightarrow\sqrt[]{\Delta'}=4\sqrt[]{5}\)
Phương trình có 2 nghiệm
\(\left[{}\begin{matrix}x=\dfrac{-8+4\sqrt[]{5}}{4}\\x=\dfrac{-8-4\sqrt[]{5}}{4}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-4\left(2-\sqrt[]{5}\right)}{4}\\x=\dfrac{-4\left(2+\sqrt[]{5}\right)}{4}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\left(2-\sqrt[]{5}\right)\\x=-\left(2+\sqrt[]{5}\right)\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=-2+\sqrt[]{5}\\x=-2-\sqrt[]{5}\end{matrix}\right.\)
c) \(4x^2+20x+4=0\)
\(\Leftrightarrow4\left(x^2+5x+1\right)=0\)
\(\Leftrightarrow x^2+5x+1=0\)
\(\Delta=25-4=21\Rightarrow\sqrt[]{\Delta}=\sqrt[]{21}\)
Phương trình có 2 nghiệm
\(\left[{}\begin{matrix}x=\dfrac{-5+\sqrt[]{21}}{2}\\x=\dfrac{-5-\sqrt[]{21}}{2}\end{matrix}\right.\)
12 tháng 9 2018
\(16x^3-12x^2+3x-7=0\)
\(\Leftrightarrow16x^3-16x^2-3x^2+3x+7x^2-7=0\)
\(\Leftrightarrow16x^2\left(x-1\right)-3x\left(x-1\right)+7\left(x-1\right)\left(x+1\right)=0\)
\(\Leftrightarrow16x^2\left(x-1\right)-3x\left(x-1\right)+\left(x-1\right)\left(7x+7\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(16x^2-3x+7x+7\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(16x^2+4x+7\right)=0\)
<=> x - 1 = 0
<=> x = 1
T
12 tháng 9 2018
\(\Leftrightarrow16x^3-16x^2+4x^2-4x+7x-7=0\)
\(\Leftrightarrow16x^2.\left(x-1\right)+4x.\left(x-1\right)+7.\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right).\left(16x^2+4x+7\right)=0\)
Ta có \(16x^2+4x+7=\left(4x\right)^2+2.4x.\frac{1}{2}+\frac{1}{4}+\frac{27}{4}\)
\(=\left(4x+\frac{1}{2}\right)^2+\frac{27}{4}>0\)
nên \(\left(x-1\right).\left(16x^2+4x+7\right)=0\)
\(\Leftrightarrow x-1=0\)
\(\Rightarrow x=1\)
30 tháng 10 2016
= 16x3 -16x2 + 4x2 - 4x + 7x - 7
= 16x2(x-1)+4x(x-1)+7(x-1)
=(x-1)(16x2+4x+7)
19 tháng 6 2021
a, 4x2 - 49 = 0
⇔⇔ (2x)2 - 72 = 0
⇔⇔ (2x - 7)(2x + 7) = 0
⇔{2x−7=02x+7=0⇔⎧⎪ ⎪⎨⎪ ⎪⎩x=72x=−72⇔{2x−7=02x+7=0⇔{x=72x=−72
b, x2 + 36 = 12x
⇔⇔ x2 + 36 - 12x = 0
⇔⇔ x2 - 2.x.6 + 62 = 0
⇔⇔ (x - 6)2 = 0
⇔⇔ x = 6
19 tháng 6 2021
e, (x - 2)2 - 16 = 0
⇔⇔ (x - 2)2 - 42 = 0
⇔⇔ (x - 2 - 4)(x - 2 + 4) = 0
⇔⇔ (x - 6)(x + 2) = 0
⇔{x−6=0x+2=0⇔{x=6x=−2⇔{x−6=0x+2=0⇔{x=6x=−2
f, x2 - 5x -14 = 0
⇔⇔ x2 + 2x - 7x -14 = 0
⇔⇔ x(x + 2) - 7(x + 2) = 0
⇔⇔ (x + 2)(x - 7) = 0
⇔{x+2=0x−7=0⇔{x=−2x=7
30 tháng 7 2021
a) Ta có: \(x^4-16x^2=0\)
\(\Leftrightarrow x^2\left(x^2-16\right)=0\)
\(\Leftrightarrow x^2\left(x-4\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\\x=-4\end{matrix}\right.\)
b) Ta có: \(x^8+36x^4=0\)
\(\Leftrightarrow x^4\left(x^4+36\right)=0\)
\(\Leftrightarrow x^4=0\)
hay x=0
c) Ta có: \(\left(x-5\right)^3-x+5=0\)
\(\Leftrightarrow\left(x-5\right)\cdot\left[\left(x-5\right)^2-1\right]=0\)
\(\Leftrightarrow\left(x-5\right)\left(x-4\right)\left(x-6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=4\\x=6\end{matrix}\right.\)
d) Ta có: \(5\left(x-2\right)-x^2+4=0\)
\(\Leftrightarrow5\left(x-2\right)-\left(x-2\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(5-x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(3-x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.\)
NT
2
NC
30 tháng 8 2020
a) Ta có: \(x^3-3x^2-16x+48=0\)
\(\Leftrightarrow x^2\left(x-3\right)-16\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x^2-16\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-3=0\\x^2-16=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3\\x=\pm4\end{cases}}\)
b) Ta có: \(10x^2-33x-7=0\)
\(\Leftrightarrow\left(10x^2-35x\right)+\left(2x-7\right)=0\)
\(\Leftrightarrow\left(2x-7\right)\left(5x+1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}2x-7=0\\5x+1=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{7}{2}\\x=-\frac{1}{5}\end{cases}}\)
30 tháng 8 2020
x3 - 3x2 - 16x + 48 = 0
<=> ( x3 - 3x2 ) - ( 16x - 48 ) = 0
<=> x2( x - 3 ) - 16( x - 3 ) = 0
<=> ( x - 3 )( x2 - 16 ) = 0
<=> ( x - 3 )( x - 4 )( x + 4 ) = 0
<=> x = 3 hoặc x = 4 hoặc x = -4
10x2 - 33x - 7 = 0
<=> 10x2 + 2x - 35x - 7 = 0
<=> ( 10x2 + 2x ) - ( 35x + 7 ) = 0
<=> 2x( 5x + 1 ) - 7( 5x + 1 ) = 0
<=> ( 5x + 1 )( 2x - 7 ) = 0
<=> \(\orbr{\begin{cases}5x+1=0\\2x-7=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{1}{5}\\x=\frac{7}{2}\end{cases}}\)
21 tháng 10 2018
\(5x^2+2y^2-6xy+16x-8y+16=0\)
\(\Rightarrow10x^2+4y^2-12xy+32x-16y+32=0\)
\(\Rightarrow\left(9x^2-12xy+4y^2\right)+\left(24x-16y\right)+16+\left(x^2+8x+16\right)=0\)
\(\Rightarrow\left(3x-2y\right)^2+2.\left(3x-2y\right).4+4^2+\left(x+4\right)^2=0\)
\(\Rightarrow\left(3x-2y+4\right)^2+\left(x+4\right)^2=0\)
\(\Rightarrow\hept{\begin{cases}3x-2y+4=0\\x+4=0\end{cases}\Rightarrow}\hept{\begin{cases}-12-2y+4=0\\x=-4\end{cases}\Rightarrow\hept{\begin{cases}y=-4\\x=-4\end{cases}}}\)
Vậy \(x=y=-4\)
18 tháng 10 2021
\(4x^3-16x^2+19x-6=0\)
\(\Leftrightarrow4x^3-8x^2-8x^2+16x+3x-6=0\)
\(\Leftrightarrow\left(x-2\right)\left(4x^2-8x+3\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(2x-3\right)\left(2x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{3}{2}\\x=\dfrac{1}{2}\end{matrix}\right.\)
`3-16x^2=0`
`<=>(\sqrt3)^2-(4x)^2=0`
`<=>(\sqrt3+4x)(\sqrt3-4x)=0`
`<=> [(\sqrt3=-4x),(\sqrt3=4x):}`
`<=> [(x=-\sqrt3/4),(x=\sqrt3/4):}`
Vậy `S={\pm \sqrt3/4}`.
Ta có: \(3-16x^2=0\)
\(\Leftrightarrow16x^2=3\)
\(\Leftrightarrow x^2=\dfrac{3}{16}\)
hay \(x\in\left\{\dfrac{\sqrt{3}}{4};-\dfrac{\sqrt{3}}{4}\right\}\)