1/2+5/14+2/63+3/108+1/156 Tính nhanh
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\(\frac{1}{2}+\frac{5}{14}+\frac{2}{63}+\frac{3}{108}+\frac{1}{156}\)\(=\frac{12}{13}\)
TL:
\(\frac{1}{2}+\frac{5}{14}+\frac{2}{63}+\frac{3}{108}+\frac{1}{156}\)
\(=\frac{12}{13}\)
\(\frac{2}{3}\cdot y-\frac{12}{3}:\left(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+\frac{2}{143}\right)=\frac{1}{3}\)\(\frac{1}{3}\)
\(\frac{2}{3}\cdot y-4:\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}+\frac{2}{11\cdot13}\right)=\frac{1}{3}\)
\(\frac{2}{3}\cdot y-4:\left(\frac{3-1}{1\cdot3}+\frac{5-3}{3\cdot5}+\frac{7-5}{5\cdot7}+\frac{9-7}{7\cdot9}+\frac{11-9}{9\cdot11}+\frac{13-11}{11\cdot13}\right)=\frac{1}{3}\)
\(\frac{2}{3}\cdot y-4:\left(1+\frac{1}{3}-\frac{1}{3}+\frac{1}{5}-\frac{1}{5}+\frac{1}{7}-\frac{1}{7}+\frac{1}{9}-\frac{1}{9}+\frac{1}{11}-\frac{1}{11}+\frac{1}{13}\right)\)\(=\frac{1}{3}\)
\(\frac{2}{3}\cdot y-4:\left(\frac{1}{1}+\frac{1}{3}\right)=\frac{1}{3}\)
\(\frac{2}{3}\cdot y-4:\frac{4}{3}\)\(=\frac{1}{3}\)
\(\frac{2}{3}\cdot y-4\cdot\frac{3}{4}=\frac{1}{3}\)
\(\frac{2}{3}\cdot y-3=\frac{1}{3}\)
\(\frac{2}{3}\cdot y=\frac{1}{3}+3\)
\(\frac{2}{3}\cdot y=\frac{10}{3}\)
\(y=\frac{10}{3}:\frac{2}{3}\)
y=5
\(\frac{29}{12}:\frac{1}{2}-\frac{5}{12}:\frac{1}{2}-\frac{1}{2}\)
= \(\left(\frac{29}{12}-\frac{5}{12}\right):\frac{1}{2}-\frac{1}{2}\)
= \(2:\frac{1}{2}-\frac{1}{2}\)
= \(4-\frac{1}{2}\)
=\(\frac{8}{2}-\frac{1}{2}\)
=\(\frac{7}{2}\)
1) a. ( 2x + 1 ) = 125
=> 2x +1 = 125
=> 2x = 125 - 1
=> 2x = 124
=> x = 124 : 2
=> x = 64
Vậy x = 64
2) 3^ 2x +1 = 243
=> 3^ 2x +1 = 3^5
=> 2x +1 = 5
=> 2x= 5-1
=> 2x = 4
=> x= 4:2
=> x = 2
Vậy x = 2
a) x4+x3+2x2+x+1=(x4+x3+x2)+(x2+x+1)=x2(x2+x+1)+(x2+x+1)=(x2+x+1)(x2+1)
b)a3+b3+c3-3abc=a3+3ab(a+b)+b3+c3 -(3ab(a+b)+3abc)=(a+b)3+c3-3ab(a+b+c)
=(a+b+c)((a+b)2-(a+b)c+c2)-3ab(a+b+c)=(a+b+c)(a2+2ab+b2-ac-ab+c2-3ab)=(a+b+c)(a2+b2+c2-ab-ac-bc)
c)Đặt x-y=a;y-z=b;z-x=c
a+b+c=x-y-z+z-x=o
đưa về như bài b
d)nhóm 2 hạng tử đầu lại và 2hangj tử sau lại để 2 hạng tử sau ở trong ngoặc sau đó áp dụng hằng đẳng thức dề tính sau đó dặt nhân tử chung
e)x2(y-z)+y2(z-x)+z2(x-y)=x2(y-z)-y2((y-z)+(x-y))+z2(x-y)
=x2(y-z)-y2(y-z)-y2(x-y)+z2(x-y)=(y-z)(x2-y2)-(x-y)(y2-z2)=(y-z)(x2-2y2+xy+xz+yz)
0,2x-2/3(x+1)=1/3
<=>0,2x-2/3x-2/3=1/3
<=>-7/15x=1
<=>x=-15/7
Vậy..............
Hok tốt
\(0,2x-\frac{2}{3}\left(x+1\right)=\frac{1}{3}\)
\(\frac{1}{5}x-\frac{2}{3}x+\frac{2}{3}=\frac{1}{3}\)
\(\left(\frac{1}{5}-\frac{2}{3}\right)x=-\frac{1}{3}\)
\(-\frac{7}{15}x=-\frac{1}{3}\)
\(x=\frac{5}{7}\)
Ta có : \(\frac{1}{2}+\frac{5}{14}+\frac{2}{63}+\frac{3}{108}+\frac{1}{156}\)
\(=\frac{1}{1.2}+\frac{5}{2.7}+\frac{2}{7.9}+\frac{3}{9.12}+\frac{1}{12.13}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}\)
\(=1-\frac{1}{13}=\frac{12}{13}\)