\(4x^2:\left(-x+1\right)\)
chia hộ mik vs
Tìm x:
c)\(x^2-4x+4=5\left(x-2\right)\))
d*)\(4x^2-12x+9=\left(5-x\right)^2\) GIÚP MIK VS MỌI NGƯỜI. MIK SẼ TÍCH.MỌI NGƯỜI TRẢ LỜI GẤP HỘ MIK
x^2 - 4x + 4 = 5 ( x - 2 )
x^2 - 4x + 4 - 5 ( x - 2 ) = 0
( x - 2 ) ^2 - 5 ( x - 2 ) = 0
( x - 2 ) ( x - 2 - 5 ) = 0
( x - 2 ) ( x - 7 ) = 0
x - 2 = 0 hoặc x - 7 = 0
x = 2 hoặc x = 7
c) (x-2)^2=5(x-2)
=> x-2=5 hoặc x-2 =0
=> x=7 hoặc x=2
d) (2x-3)^2=(5-x)^2
=> 2x-3=5-x
=> x=8/3
4x^2 - 12x + 9 = ( 5 - x ) ^2
( 2x - 3 ) ^2 = ( 5 - x ) ^2
( 2x - 3 ) ^2 - ( 5 - x ) ^2 = 0
( 2x - 3 - 5 + x ) ( 2x - 3 + 5 - x ) = 0
( 3x - 8 ) ( x + 2 ) = 0
3x - 8 = 0 hoặc x + 2 = 0
x = 8/3 hoặc x = -2
tìm GTNN biết \(\left(x^z+1\right)^2+\left(y^z+2\right)^4-2\)
hộ mik vs mik đg cần gấp
x^2+1>=1
=>(x^2+1)^2>=1
y^2+2>=2
=>(y^2+2)^4>=16
=>(x^2+1)^2+(y^2+2)^4>=17
=>(x^2+1)^2+(y^2+2)^4-2>=15
Dấu = xảy ra khi x=y=0
Giải hộ vs \(\hept{\begin{cases}x^2\left(y+1\right)\left(y+x+1\right)=3x^2-4x-1\\x\left(y+1\right)+1=x^2\end{cases}}\)
\(1.\left(x^2-1\right)^2-x\left(x^2-1\right)-2x^2=0\)
\(2.\left(x^2+4x+8\right)^2+3x\left(x^2+4x+8\right)+2x^2=0\)
\(3.4\left(x^2+x+1\right)^2+5x\left(x^2+x+1\right)+x^2=0\)
Giair phương trình hộ mik nhé đúng mik tick cho
1) Ta có: \(\left(x^2-1\right)^2-x\left(x^2-1\right)-2x^2=0\)
\(\Leftrightarrow\left[\left(x^2-1\right)^2+x\left(x^2-1\right)\right]-\left[2x\left(x^2-1\right)+2x^2\right]=0\)
\(\Leftrightarrow\left(x^2-1\right)\left(x^2+x-1\right)-2x\left(x^2+x-1\right)=0\)
\(\Leftrightarrow\left(x^2-2x-1\right)\left(x^2+x-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x^2-2x-1=0\\x^2+x-1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}\left(x-1\right)^2=2\\\left(x+\frac{1}{2}\right)^2=\frac{5}{4}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-1=\pm\sqrt{2}\\x+\frac{1}{2}=\pm\frac{\sqrt{5}}{2}\end{cases}}\Rightarrow\orbr{\begin{cases}x=1\pm\sqrt{2}\\x=-\frac{1\pm\sqrt{5}}{2}\end{cases}}\)
2) Ta có: \(\left(x^2+4x+8\right)^2+3x\left(x^2+4x+8\right)+2x^2=0\)
\(\Leftrightarrow\left[\left(x^2+4x+8\right)^2+x\left(x^2+4x+8\right)\right]+\left[2x\left(x^2+4x+8\right)+2x^2\right]=0\)
\(\Leftrightarrow\left(x^2+4x+8\right)\left(x^2+5x+8\right)+2x\left(x^2+5x+8\right)=0\)
\(\Leftrightarrow\left(x^2+6x+8\right)\left(x^2+5x+8\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x+4\right)\left(x^2+5x+8\right)=0\)
Vì \(x^2+5x+8=\left(x^2+5x+\frac{25}{4}\right)+\frac{7}{4}=\left(x+\frac{5}{2}\right)^2+\frac{7}{4}>0\)
\(\Rightarrow\orbr{\begin{cases}x+2=0\\x+4=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-2\\x=-4\end{cases}}\)
Vậy x = -2 hoặc x = -4
P/s: Bạn Thùy Linh nếu PT chứa nghiệm vô tỉ thì với trình độ bình thường không dễ tìm được nghiệm đâu nhé
3) Ta có: \(4\left(x^2+x+1\right)^2+5x\left(x^2+x+1\right)+x^2=0\)
\(\Leftrightarrow\left[4\left(x^2+x+1\right)^2+4x\left(x^2+x+1\right)\right]+\left[x\left(x^2+x+1\right)+x^2\right]=0\)
\(\Leftrightarrow4\left(x^2+x+1\right)\left(x^2+2x+1\right)+x\left(x^2+2x+1\right)=0\)
\(\Leftrightarrow\left(4x^2+4x+4+x\right)\left(x^2+2x+1\right)=0\)
\(\Leftrightarrow\left(4x^2+5x+4\right)\left(x+1\right)^2=0\)
Xét PT \(4x^2+5x+4=0\) ta có:
\(\Delta_x=5^2-4\cdot4\cdot4=-39< 0\)
\(\Rightarrow\left(x+1\right)^2=0\Rightarrow x=-1\)
Vậy x = -1
Tìm x
\(\left(4x-1\right)^3+\left(3-4x\right)\left(9+12x+16x^2\right)=\left(8x-1\right)\left(8x+1\right)-\left(3x-5\right)\)
GIÚP MIK VS
Rút gọn biểu thức :
P= \(^{ }\left(x-y\right)^2\)+ \(\left(x+y\right)^2\)-2 (x+y) (x-y) \(-4x^2\)
Mọi ng ơi hộ mik vs mk đng cần
ta có ;
\(P=\left(x-y\right)^2+\left(x+y\right)^2-2\left(x-y\right)\left(x+y\right)-4x^2=\left(x-y+x+y\right)^2-4x^2\)
\(=\left(2x\right)^2-4x^2=0\)
\(\Rightarrow P=x^2-2xy+y^2+x^2+2xy+y^2-2\left(x^2-y^2\right)-4x^2\)\(4x^2\)
\(\Rightarrow P=2x^2+2y^2-2x^2-2y^2-4x^2\)
\(\Rightarrow P=-4x^2\)
Giải các phương trình sau:
a) \(\left(4x-1\right)\left(x-3\right)=\left(x-3\right)\left(5x+2\right)\).
b)\(\left(x+3\right)\left(x-5\right)+\left(x+3\right)\left(3x-4\right)=0\)
c)\(\left(1-x\right)\left(5x+3\right)=\left(3x-7\right)\left(x-1\right)\). Giải chi tiết hộ mik nhoa, mik tik
TA CÓ:
\(a,\left(4x-1\right)\left(x-3\right)=\left(x-3\right)\left(5x+2\right)\Leftrightarrow\left(4x-1\right)\left(x-3\right)-\left(x-3\right)\left(5x+2\right)=0\)
\(\left(x-3\right)\left(4x-1-5x-2\right)=0\Leftrightarrow\left(x-3\right)\left(-x-3\right)=0\orbr{\begin{cases}x=3\\x=-3\end{cases}}\)
\(b,\left(x+3\right)\left(x-5\right)+\left(x+3\right)\left(3x-4\right)=0\Leftrightarrow\left(x+3\right)\left(x-5+3x-4\right)=0\)
\(\left(x-3\right)\left(4x-9\right)=0\orbr{\begin{cases}x=3\\x=\frac{9}{4}\end{cases}}\)
\(c,\left(1-x\right)\left(5x+3\right)=\left(3x-7\right)\left(x-1\right)\Leftrightarrow\left(1-x\right)\left(5x+3\right)=\left(7-3x\right)\left(1-x\right)\)
\(\left(1-x\right)\left(5x+3-7+3x\right)=0\Leftrightarrow\left(1-x\right)\left(8x-4\right)=0\orbr{\begin{cases}x=1\\x=\frac{1}{2}\end{cases}}\)
\(\left(\frac{2x-x^2}{2x^2+8}-\frac{2x^2}{x^3-2x^2+4x-8}\right)\left(\frac{2}{x^3}+\frac{1-x}{x}\right)\) ) ae giúp mik vs nhé mik cần gấp kết quả vs cách lm ngắn gọn nhất của bài này ạ
\(\hept{\begin{cases}x^2-5y^2-8y=3\\\left(2x+4y-1\right)\sqrt{2x-y-1}=\left(4x-2y-3\right)\sqrt{x+2y}\end{cases}}\)
giải hộ mk hpt này vs , mk cảm ơn
ĐKXĐ: \(2x-y-1\ge0;x+2y\ge0\)
Đặt \(\sqrt{2x-y-1}=a;\sqrt{x+2y}=b\left(a,b\ge0\right)\). Khi đó ta có:
\(\left(2b^2-1\right)a=\left(2a^2-1\right)b\Leftrightarrow\left(a-b\right)\left(2ab+1\right)=0\)
\(\Leftrightarrow a=b\) hoặc \(2ab+1=0\)(loại vì \(a,b\ge0\))
Suy ra: \(\sqrt{2x-y-1}=\sqrt{x+2y}\Leftrightarrow x=3y+1\)
Pt đầu tiên trở thành: \(\left(3y+1\right)^2-5y^2-8y=3\)
\(\Leftrightarrow\left(y-1\right)\left(2y+1\right)=0\Leftrightarrow\orbr{\begin{cases}y=1\\y=-\frac{1}{2}\end{cases}}\)
+) Với \(y=1\Rightarrow x=4\Rightarrow\left(x;y\right)=\left(4;1\right)\)(tm)
+) Với \(y=-\frac{1}{2}\Rightarrow x=-\frac{1}{2}\Rightarrow\left(x;y\right)=\left(-\frac{1}{2};-\frac{1}{2}\right)\) (loại)
Vậy hpt có nghiệm duy nhất \(\left(x;y\right)=\left(4;1\right).\)
a,\(\left(4.\sqrt{x-1}-7\right).\left(2-\sqrt{x-1}\right)=5-4x\)
b,\(\frac{2}{5}.\left(\sqrt{2x+1}+5\right)=\frac{1}{4}.\left(\sqrt{2x+1}-1\right)\)
mn ơi giúp mik vs :((