3x+1 . 3x+3= 810
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\(1,\\ a,=x^2+6x+9-x^2-6x=9\\ b,=3x-1+6x-9x^2+x-10=-9x^2+10x-11\\ 2,\\ a,=4xy\left(x^2-2xy+y^2\right)=4xy\left(x-y\right)^2\)
Đề trước đó:
(x-7)(x+1)-(x-3)^2=(3x-5)(3x+5)-(3x+1)^2+(x-2)^2-x
<=>x^2+x-7x-7-x^2+6x-9=9x^2-25-9x^2-6x-1+x^2-4x+4-x
<=>x^2-11x-6=0
<=>x^2-2x. 11/2 + 121/4-145/4=0
<=>(x-11/2)^2=145/4
<=>|x-11/2|=căn(145)/2
<=>x=[11+-căn(145)]/2
b.x^3+y^3+3x^2+3x+1=(x^3+3x^2+3x+1)+y^3
=(x+1)^3+y^3
=(x+1+y).((x+1)^2-x+1.y+y^2))
Phần b trước nà
1)\(25x+3\left(4-6x\right)=50\)
\(25x+12-18x=50\)
\(7x+12=50\)
\(7x=38\)
\(x=\frac{38}{7}\)
2)\(4\left(2x+3\right)+2\left(3x+1\right)=120\)
\(8x+12+6x+2=120\)
\(14x+14=120\)
\(14x=106\)
\(x=\frac{53}{7}\)
\(x^3-3x^2-3x-1=\left(x-4\right)\left(x^2+x+1\right)+3\)
\(\Rightarrow x^3-3x^2-3x-1\) chia hết \(x^2+x+1\) khi \(3⋮x^2+x+1\)
\(\Rightarrow x^2+x+1=Ư\left(3\right)\) (1)
Mà x nguyên dương \(\Rightarrow x^2+x+1\ge1^2+1+1=3\) (2)
(1);(2) \(\Rightarrow x^2+x+1=3\)
\(\Rightarrow x=1\)
a) [ 3x-1] + 4x - 3 = 7
3x - 1 + 4x = 7 + 3 = 10
( 3 + 4 )x - 1 =10
7x - 1 = 10
7x=11
x=11/7
Câu tiếp theo làm tương tự nhé =))
) [ 3x-1] + 4x - 3 = 7
3x - 1 + 4x = 7 + 3 = 10
( 3 + 4 )x - 1 =10
7x - 1 = 10
7x=11
x=11/7
\(\Leftrightarrow2x\left(x+5\right)-3\left(x-2\right)=7x+1\)
\(\Leftrightarrow2x^2+10x-3x+6-7x-1=0\)
\(\Leftrightarrow2x^2+5=0\)(vô lý)
ĐKXĐ:\(\left\{{}\begin{matrix}x\ne2\\x\ne-5\end{matrix}\right.\)
\(\dfrac{2x}{x-2}-\dfrac{3}{x+5}=\dfrac{7x+1}{x^2+3x-10}\\ \Leftrightarrow\dfrac{2x\left(x+5\right)}{\left(x+5\right)\left(x-2\right)}-\dfrac{3\left(x-2\right)}{\left(x+5\right)\left(x-2\right)}=\dfrac{7x+1}{x^2-2x+5x-10}\\ \Leftrightarrow\dfrac{2x^2+10x}{\left(x+5\right)\left(x-2\right)}-\dfrac{3x-6}{\left(x+5\right)\left(x-2\right)}=\dfrac{7x+1}{x\left(x-2\right)+5\left(x-2\right)}\\ \Leftrightarrow\dfrac{2x^2+10x}{\left(x+5\right)\left(x-2\right)}-\dfrac{3x-6}{\left(x+5\right)\left(x-2\right)}-\dfrac{7x+1}{\left(x+5\right)\left(x-2\right)}=0\)
\(\Leftrightarrow\dfrac{2x^2+10x-3x+6-7x-1}{\left(x+5\right)\left(x-2\right)}=0\\ \Leftrightarrow\dfrac{2x^2+5}{\left(x+5\right)\left(x-2\right)}=0\\ \Rightarrow2x^2+5=0\left(vô.lí\right)\)
Vậy pt vô nghiệm
3^x+1 . 3^x+3 = 810
3^(x+1+x+3) = 810
3^(2x+4) = 810
3(2x+4) =
\(3^{x+1}.3^{x+3}\)\(=810\)
\(3^{x+1}\) \(\left(1+9\right)=810\) \(=>3^{x+1}=81=>x+3=4=>x=3\)