Hãy rút gọn biểu thức : 3(x-1) - 2Ix-3I
Ai tl đúng mk tick nhé
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\(A=3\left(2x-1\right)-\left|x-5\right|\)
\(=6x-3-\left|x-5\right|\)
TH1 : \(x-5\ge0\Rightarrow x\ge5\Rightarrow\left|x-5\right|=x-5\)
\(A=6x-3-x+5\)
\(=5x+2\)
TH2 : \(x-5< 0\Rightarrow x< 5\Rightarrow\left|x-5\right|=5-x\)
\(A=6x-3-5+x\)
\(=7x-8\)
Vậy ....
\(A=x^3-8-\left(x^3+3x^2+3x+1\right)+3\left(x^2-1\right)\)
\(=x^3-8-x^3-3x^2-3x-1+3x^2-3\)
\(=\left(x^3-x^3\right)+\left(-3x^2+3x^2\right)-3x-8-3\)
\(=-3x-11\)
\(\frac{3}{1.2.3}+\frac{3}{2.3.4}+\frac{3}{3.4.5}+...+\frac{3}{15.16.17}\)
=\(\frac{3}{1.2.3}+\frac{3}{2.3.4}+\frac{3}{3.4.5}+...+\frac{3}{3.5.16.17}\)
=\(\frac{1}{1.2}+\frac{1}{2.4}+\frac{1}{4.5}+...+\frac{1}{5.16.17}\)
\(\left(x-1\right)\left(x+2\right)+\left(x+1\right)x=x^2+2x-x-2+x^2+x=\left(x^2+x^2\right)+\left(2x-x+x\right)-2=2x^2+2x-2=2\left(x^2+x-1\right)\)
a) 3(x-1)-2|x+3| = 3x-3-2(x+3) = 3x-3-2x+6 = (3x-2x)+(6-3)=x+3
b) 2|x-3|-|4x-1| = 2(x-3)-(4x-1) = 2x-6-4x+1 = (2x-4x)-(6-1) = -2x-5
a) \(\left(x-3\right)^2.\left(x+3\right).\left(x-3\right)\)
\(=\left(x-3\right).\left(x-3\right).\left(x+3\right).\left(x-3\right)\)
\(=\left(x-3\right)^3.\left(x+3\right)\)
\(=\left(3x-9\right).\left(x+3\right)\)
Phần b tương tự
`A=1+4+4^2+4^3+....+4^99+4^100`
`=>4A=4+4^2+4^3+4^4+...+4^100+4^101`
`=>4A-A=4^101-1`
`=>3A=4^101-1`
`=>A=(4^101-1)/3`
Ta có: \(A=1+4+4^2+...+4^{99}+4^{100}\)
\(\Leftrightarrow4\cdot A=4+4^2+4^3+...+4^{100}+4^{101}\)
\(\Leftrightarrow4\cdot A-A=4^{101}-1\)
hay \(A=\dfrac{4^{101}-1}{3}\)
Xét 2 trường hợp :
TH1 : x ≥ 0 => |x - 3| = x - 3
=> 3(x - 1) - 2|x - 3| = 3(x - 1) - 2(x - 3)
= 3x - 3 - 2x + 6
= x + 3
TH2 : x < 0 => |x - 3| = 3 - x
=> 3(x - 1) - 2|x - 3| = 3(x - 1) - 2(3 - x)
= 3x - 3 - 6 + 2x
= 5x - 9
Vậy 3(x - 1) - 2|x - 3| = x + 3 hoặc 3(x - 1) - 2|x - 3| = 5x - 9
Tks bn nhé