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\(\text{a) }\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+.....+\frac{1}{98.99.100}\right)x=-3\)
\(\Rightarrow\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+.....+\frac{1}{98.99}-\frac{1}{99.100}\right)x=-3\)
\(\Rightarrow\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{99.100}\right)x=-3\)
\(\Rightarrow\frac{1}{2}\left(\frac{1}{2}-\frac{1}{9900}\right)x=-3\)
\(\Rightarrow\frac{1}{2}.\left(\frac{4950}{9900}-\frac{1}{9900}\right)x=-3\)
\(\Rightarrow\left(\frac{1}{2}.\frac{4949}{9900}\right).x=-3\)
\(\Rightarrow\frac{4949}{19800}x=-3\)
\(\Rightarrow x=\left(-3\right).\frac{19800}{4949}\)
\(\Rightarrow x=\frac{-59400}{4949}\)
P/s : ko chắc nha
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A =15/x+2 + 14/x+2 = 29/x+2
b) x+2 là U(29) = { -1;1;-29;29}
=> x ={ -3;-1;-31;27}
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a) Để \(\frac{3}{x-1}\inℤ\Rightarrow\left(x-1\right)\inƯ\left(3\right)=\left\{\pm1;\pm3\right\}\)
\(\Rightarrow x\in\left\{-2;0;2;4\right\}\)
b) Để \(\frac{4}{2x-1}\inℤ\Rightarrow\left(2x-1\right)\inƯ\left(4\right)=\left\{\pm1;\pm2;\pm4\right\}\)
=> \(2x\in\left\{-3;-1;0;2;3;5\right\}\)
=> \(x\in\left\{-\frac{3}{2};-\frac{1}{2};0;1;\frac{3}{2};\frac{5}{2}\right\}\)
c) Ta có: \(\frac{3x+7}{x-7}=\frac{\left(3x-21\right)+28}{x-7}=2+\frac{28}{x-7}\)
Xong xét các TH như a,b nhé
thanks nhưng mai mik mới t.i.k đc bạn
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A= x+2+1/x+2
A=1+1/x+2
vi 1 la so nguyen nen A nguyen <=> 1/x+2 nguyen <=> (x+2) thuoc U(1)={+-1)
<=>x+2=-1 hoac x+2=1
<=>x=-3 hoac x=-1
vay x thuoc {-3:-1}
hoc tot
de A co gia tri nguyen
=> ( x + 3 ) chia het cho ( x+2)
=> ( x +2 + 3-2 ) chia het (x +2)
=> ( x+2 )-1 chia het (x+2)
ma (x +2) chia het cho (x+2)
=> 1chia het (x+2)
=> x+2 thuoc U(1)
=> x+2 thuoc ( 1 ; -1)
=> x thuoc ( 3 ; 1 )
mik ko viet dau cho nhanh nha
ban ghi ki hieu thuoc chu dung ghi chu nhu mik ca dau chia het cung the nha
hok tot
Để \(\frac{3}{x+1}\)nhận giá trị nguyên thì
\(\Leftrightarrow3⋮x+1\)
Mà x\(\in Z\Rightarrow x+1\in Z\)
\(\Rightarrow x+1\inƯ\left(3\right)=\left\{\pm1;\pm3\right\}\)
Ta có bảng giá trị
Đối chiếu điều kiện x\(\in Z\)
Vậy x={-2;-4;0;2}
\(\frac{3}{x+1}\) có giá trị nguyên
\(\Leftrightarrow3⋮x+1\)
\(\Rightarrow x+1\inƯ\left(3\right)\)
\(\Rightarrow x+1\in\left\{-1;1;-3;3\right\}\)
\(\Rightarrow x\in\left\{-2;0;-4;2\right\}\)