CM các phân số sau tối giản với mọi n thuộc số tự nhiên"
a) \(\frac{12n+1}{2\left(10n+1\right)}\)
b)\(\frac{2n+3}{2n^2+4n+1}\)
CM các phân số sau tối giản với mọi n thuộc số tự nhiên"
a) \(\frac{12n+1}{2\left(10n+1\right)}\)
b)\(\frac{2n+3}{2n^2+4n+1}\)
Tính giá trị của biểu thức sau , biết rằng a+b+c=0 :
\(A=\left(\frac{a-b}{c}+\frac{b-c}{a}+\frac{c-a}{b}\right)\left(\frac{c}{a-b}+\frac{a}{b-c}+\frac{b}{c-a}\right).\)
Gọi \(M=\frac{a-b}{c}+\frac{b-c}{a}+\frac{c-a}{b},\)ta có :
\(M.\frac{c}{a-b}=1+\frac{c}{a-b}\left(\frac{b-c}{a}+\frac{c-a}{b}\right)=1+\frac{c}{a-b}.\frac{b^2-bc+ac-a^2}{ab}\)
\(=1+\frac{c}{a-b}.\frac{\left(a-b\right)\left(c-a-b\right)}{ab}=1+\frac{2c^2}{ab}=1+\frac{2c^3}{abc}\)
Tương tự : \(M.\frac{a}{b-c}=1+\frac{2a^3}{abc},M.\frac{b}{c-a}=1+\frac{2b^3}{abc}.\)
Vậy \(A=3+\frac{2\left(a^3+b^3+c^3\right)}{abc}=9\)
tìm x,biết
a) 3x2 - 27x = 0
b) 2/3x ( x2 - 4) = 0
\(3x^2-27x=0\)
\(3x\left(x-9\right)=0\)
\(\left[\begin{array}{nghiempt}x=0\\x-9=0\end{array}\right.\)
\(\left[\begin{array}{nghiempt}x=0\\x=9\end{array}\right.\)
\(\frac{2}{3}x\left(x^2-4\right)=0\)
\(\frac{2}{3}x\left(x-2\right)\left(x+2\right)=0\)
\(\left[\begin{array}{nghiempt}x=0\\x-2=0\\x+2=0\end{array}\right.\)
\(\left[\begin{array}{nghiempt}x=0\\x=2\\x=-2\end{array}\right.\)
a)\(3x^2-27x=0\)
\(3x\left(x-9\right)=0\)
\(\Rightarrow\left[\begin{array}{nghiempt}3x=0\\x-9=0\end{array}\right.\Rightarrow\left[\begin{array}{nghiempt}x=0\\x=9\end{array}\right.\)
b) \(\frac{2}{3}x\left(x^2-4\right)=0\)
\(\frac{2}{3}x\left(x+2\right)\left(x-2\right)=0\)
\(\Rightarrow\left[\begin{array}{nghiempt}\frac{2}{3}x=0\\x+2=0\\x-2=0\end{array}\right.\Rightarrow\left[\begin{array}{nghiempt}x=0\\x=-2\\x=2\end{array}\right.\)
Phân tích đa thức thành nhân tử :
a) 25x2 - 10y + 1 - x2
b) 4y2 - 4x2 - 4y + 1
c) -y2 + 6y - 9 + x2
\(25x^2-10x+1-y^2\)
\(=\left(5x-1\right)^2-y^2\)
\(=\left(5x-y-1\right)\left(5x+y-1\right)\)
\(4y^2-4x^2-4y+1\)
\(=\left(2y-1\right)^2-\left(2x\right)^2\)
\(=\left(2y+2x-1\right)\left(2y-2x-1\right)\)
\(-y^2+6y-9+x^2\)
\(=x^2-\left(y-3\right)^2\)
\(=\left(x+y-3\right)\left(x-y+3\right)\)
Cho a, b, c thõa mãn : a.b.c = 2016
Tính : \(A=\frac{2016.a}{ab+2016.a+2016}+\frac{b}{bc+b+2016}+\frac{c}{ac+c+1}\)
\(A=\frac{2016a}{ab+2016a+2016}+\frac{b}{bc+b+2016}+\frac{c}{ac+c+1}\)
\(A=\frac{2016a}{ab+2016a+abc}+\frac{b}{bc+b+2016}+\frac{bc}{abc+bc+b}\)
\(A=\frac{2016a}{a\left(b+2016+bc\right)}+\frac{b}{bc+b+2016}+\frac{bc}{2016+bc+b}\)
\(A=\frac{2016}{b+2016+bc}+\frac{b}{bc+b+2016}+\frac{bc}{2016+bc+b}\)
\(A=\frac{2016+b+bc}{2016+b+bc}=1\)
Thay : 2016 = abc
ta có :
\(A=\frac{a^2bc}{ab+a^2bc+abc}+\frac{b}{bc+b+abc}+\frac{c}{ac+c+1}\)
\(A=\frac{a^2bc}{ab\left(1+ac+c\right)}+\frac{b}{b\left(c+1+ac\right)}+\frac{c}{ac+c+1}\)
\(A=\frac{ac}{ac+c+1}+\frac{1}{ac+c+1}+\frac{c}{ac+c+1}\)
\(A=\frac{ac+c+1}{ac+c+1}\)
\(A=1\)
vậy \(A=\frac{2016.a}{ab+2016.a+2016}+\frac{b}{bc+b+2016}+\frac{c}{ac+c+1}=1\)
Chúc bạn học tốt !
Xác định các số hữu tỉ p và q để đa thức x3+px+q chia heets cho đa thức x2-2x-3
GIÚP MIK VS MIK CẦN GẤP LẮM MAI PHẢI NỘP RÔI
cho các số x,y thỏa mãn đẳng thức: 3x2+3y2+4xy+2x-2y+2=0
tính giá trị biểu thức : M =(x+y)2013+(x+2)2014+(y-1)2015
\(\left(\frac{1}{x+1}-\frac{3}{x^3+1}+\frac{3}{x^2-x+1}\right).\frac{3x^2-3x+3}{\left(x+1\right)\left(x+2\right)}-\frac{2x-2}{x^2+2x}\) thực hiện phép tính
\(\left(\frac{1}{x+1}-\frac{3}{x^3+1}+\frac{3}{x^2-x+1}\right)\times\frac{3x^2-3x+3}{\left(x+1\right)\left(x+2\right)}-\frac{2x-2}{x^2+2x}\)
\(=\left[\frac{x^2-x+1}{\left(x+1\right)\left(x^2-x+1\right)}-\frac{3}{\left(x+1\right)\left(x^2-x+1\right)}+\frac{3\left(x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}\right]\times\frac{3\left(x^2-x+1\right)}{\left(x+1\right)\left(x+2\right)}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
\(=\frac{\left(x^2-x+1\right)-3+3\left(x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}\times\frac{3\left(x^2-x+1\right)}{\left(x+1\right)\left(x+2\right)}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
\(=\frac{x^2-x+1-3+3x+3}{x+1}\times\frac{3}{\left(x+1\right)\left(x+2\right)}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
\(=\frac{x^2+2x+1}{x+1}\times\frac{3}{\left(x+1\right)\left(x+2\right)}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
\(=\frac{3\left(x+1\right)^2}{\left(x+1\right)\left(x+1\right)\left(x+2\right)}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
\(=\frac{3x}{x\left(x+2\right)}-\frac{2x-2}{x\left(x+2\right)}\)
\(=\frac{3x-2x+2}{x\left(x+2\right)}\)
\(=\frac{x+2}{x\left(x+2\right)}\)
\(=\frac{1}{x}\)
1. Tính
\(P=\frac{1}{x^2+5x+6}+\frac{1}{x^2+7x+12}+\frac{1}{x^2+9x+20}+\frac{1}{x^2+11x+30}\)
\(P=\frac{1}{x^2+2x+3x+6}+\frac{1}{x^2+3x+4x+12}+\frac{1}{x^2+4x+5x+20}+\frac{1}{x^2+5x+6x+30^{ }}\)
\(P=\frac{1}{\left(x^2+2x\right)+\left(3x+6\right)}+\frac{1}{\left(x^2+3x\right)+\left(4x+12\right)}+\frac{1}{\left(x^2+4x\right)+\left(5x+20\right)}+\frac{1}{\left(x^2+5x\right)+\left(6x+30\right)}\)
\(P=\frac{1}{x\left(x+2\right)+3\left(x+2\right)}+\frac{1}{x\left(x+3\right)+4\left(x+3\right)}+\frac{1}{x\left(x+4\right)+5\left(x+4\right)}+\frac{1}{x\left(x+5\right)+6\left(x+5\right)}\)
\(P=\frac{1}{\left(x+2\right)\left(x+3\right)}+\frac{1}{\left(x+3\right)\left(x+4\right)}+\frac{1}{\left(x+4\right)\left(x+5\right)}+\frac{1}{\left(x+5\right)\left(x+6\right)}\)
\(P=\frac{1}{x+2}-\frac{1}{x+3}+\frac{1}{x+3}-\frac{1}{x+4}+\frac{1}{x+4}-\frac{1}{x+5}+\frac{1}{x+5}-\frac{1}{x+6}\)
\(P=\frac{1}{x+2}-\frac{1}{x+6}\)
\(P=\frac{x+6}{\left(x+2\right)\left(x+6\right)}-\frac{x+2}{\left(x+2\right)\left(x+6\right)}\)
\(P=\frac{x+6-x+2}{\left(x+2\right)\left(x+6\right)}\)
\(P=\frac{4}{\left(x+2\right)\left(x+6\right)}\)
Chúc cậu học tốt nha !
P= 1/ x2+5x+6 + 1/ x2+ 7x+12 + 1/x2+9x+20 +1/ x2+11x+30
P=1/ x2+2x+3x+6 + 1/ x2+3x+4x+12 + 1/ x 2+4x+5x+20 + 1/ x2+6x+5x+30
P=1/x.(x+2) + 3.(x+2) + 1/ x.(x+3)+4.(x+3) + 1/ x.(x+4) + 5.(x+4) + 1/ x.(x+6)+5.(x +6)
P= 1/ (x+2).(x+3) + 1/(x+3).(x+4)+1/ ( x+4).(x+5)+1/(x+6).(x+5)
P=1.(x+4)(x+5)(x+6) /(x+2)(x+3)(x+4).(x+5)(x+6) + 1.(x+2)(x+5)(x+6)/ ( x+2)(x+3)(x+4)(x+5)(x+6) + 1(x+2)(x+3)(x+6)/ (x+2)(x+3)(x+4)(x+5)(x+6) +1.(x+2)(x+3)(x+4)/(x+2)(x+3)(x+4)(x+5)(x+6)
P = (x+4)(x+5)(x+6)+(x+2)(x+5)(x+6)+(X+2)(x+3)(x+6)+(x+2)(x+3)(x+4)/(x+2)(x+3)(x+4)(x+5)(x+6)
P=4/(x+2)(x+6)
Sorry .mk tính sai kết quả phải là 2/(x+2).(x+6) còn phần trên đúng rồi
Bài 1: CMR:
Nếu 10x^2 + 5xy - 3y^2 =0 thì 2x-y/3x-y + 5y-x/3x+y = -3
Bài 2: Tìm các giá trị của số nguyên x sao cho:
1/x + 1/x+2 + x-2/x^2 + 2x nhận giá trị nguyên
Bài 3: Tìm a,b biết:
a) 1/x^2 - 4 = 9/x-2 + b/x+2
b) 1/x^3 +1 = a/x+1 + bx + c/x^2 -x +1
giúp mình vs m.n ơi