x(x - 4) = 320
<=>x2 - 4x - 320 = 0
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320-4x+43=352
4x+64=320-352
4x+64=-32
4x=-32-64
4x=-96
x=-96:4
x=-24
4(x-3)2-320 = 0
=> 4(x-3)2 = 320
=> (x-3)2 = 320 : 4 = 80 = (8,94427191)2 = (-8,94427191)2
TH1:
x - 3 = 8,94427191
=> x = 11,94427191
TH2:
x - 3 = -8,94427191
=> x = -5,94427191
7(4+x)3-875 = 0
=> 7(4+x)3 = 875
=> (4+x)3 = 875:7 = 125 = 53
=> 4 + x = 5
=> x = 1
650 - 5(x+4)2 = 330
5(x+4)2 = 650 - 330 =320
=> (x+4)2 = 320 : 5 = 64 = 82
=> x+4 = 8
=> x = 4
3(5-x)2-15 = 60
=> 3(5-x)2 = 75
=> (5-x)2 = 25 = 52 =(-5)2
TH1:
5-x =5
=> x = 0
TH2: 5-x = -5
=> x = 10
\(2x\left(x-17\right)+\left(17-x\right)=0\)
\(\Leftrightarrow\left(2x-1\right)\left(x-17\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=17\end{cases}}\)
a) x = 320 - y
y = 320 - x
b) 4x - y = 960
4x = 960 + y
x = ( 960 + y ) : 4
x+y=320(*)
4x-y=960(**)
=> x+y+4x-y=320+960
=>5x=1280
=>x=256
Thay x=256 vào (*) suy ra y=64
Thử lại vào (**) thỏa mãn
Vậy x=256
y=64
a) \(^{x^3}\) - 7x+6=0
\(\Leftrightarrow\) \(^{x^3}\) - x-6x+6=0
\(\Leftrightarrow\) \(\left(x^3-x\right)\) - \(\left(6x-6\right)\) =0
\(\Leftrightarrow\) x\(\left(x^2-1\right)\) - 6\(\left(x-1\right)\) =0
\(\Leftrightarrow\) x\(\left(x+1\right)\)\(\left(x-1\right)\) - 6\(\left(x-1\right)\) =0
\(\Leftrightarrow\) \(\left(x-1\right)\) \(\left[x-6\left(x+1\right)\right]\) =0
\(\Leftrightarrow\) \(\left(x-1\right)\) \(\left(6-5x\right)\) =0
\(\Leftrightarrow\) \(\left[\begin{matrix}x-1=0\\6-5x=0\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left[\begin{matrix}x=1\\5x=-6\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left[\begin{matrix}x=1\\x=-\frac{6}{5}\end{matrix}\right.\)
Những câu sau dùng phương pháp phân tích đa thức thành nhân tử nhé!
\(4x^2+4x-3=0\)
\(\left[\left(2x\right)^2+2.2x.1+1\right]-4=0\)
\(\left(2x+1\right)^2-2^2=0\)
\(\left(2x+1-2\right).\left(2x+1+2\right)=0\)
\(\left(2x-1\right).\left(2x+3\right)=0\)
\(\Rightarrow\orbr{\begin{cases}2x-1=0\\2x+3=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=-\frac{3}{2}\end{cases}}}\)
Vậy \(\orbr{\begin{cases}x=\frac{1}{2}\\x=-\frac{3}{2}\end{cases}}\)
\(x^4-3x^3-x+3=0\)
\(x^3.\left(x-3\right)-\left(x-3\right)=0\)
\(\left(x-3\right).\left(x^3-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-3=0\\x^3-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=3\\x=1\end{cases}}}\)
Vậy \(\orbr{\begin{cases}x=3\\x=1\end{cases}}\)
\(x^2.\left(x-1\right)-4x^2+8x-4=0\)
\(x^2.\left(x-1\right)-\left[\left(2x\right)^2-2.2x.2+2^2\right]=0\)
\(x^2.\left(x-1\right)-\left(2x-2\right)^2=0\)
\(x^2.\left(x-1\right)-4.\left(x-1\right)^2=0\)
\(\left(x-1\right).\left[x^2-4.\left(x-1\right)\right]=0\)
\(\left(x-1\right).\left[x^2-2.x.2+2^2\right]=0\)
\(\left(x-1\right).\left(x-2\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-1=0\\x-2=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=1\\x=2\end{cases}}}\)
Vậy \(\begin{cases}x=1\\x=2\end{cases}\)
Tham khảo nhé~
\(x^2-4x-320=0\)
\(\Leftrightarrow x^2-20x+16x-320=0\)
\(\Leftrightarrow x\cdot\left(x-20\right)+16\left(x-20\right)=0\)
\(\Leftrightarrow\left(x-20\right)\left(x+16\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-20=0\\x+16=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=20\\x=-16\end{matrix}\right.\)