1+2+5=
1+2+1+2+1+2+1+2+1+2+1+2+1+2+1+2+1+2+1+2+1+2+1+2+1+2+1+2+1+2+1+2+1+2+1+2+1+2+1+2+1+2+1+2=
5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5=
...................=66
...................=110
1+2+........+1+2 = 66
5+5+........+5+5 = 220
k mk nha
Rút gọn : a . P = 3+2√3 / √3 + 2+√2 / √2+1 - ( √2 + √3 ) ; b. N = ( 1 - 5 + √5 / 1 + √5 ) ( 5 - √5 / 1- √5 - 1 ) ; c. Q = ( 5 - 2√5 / 2 - √5 - 2 ) ( 3+3 √5 / 3 + √5 - 2 ). Giúp mik vs ạ
a: \(P=\dfrac{\sqrt{3}\left(2+\sqrt{3}\right)}{\sqrt{3}}+\dfrac{\sqrt{2}\left(\sqrt{2}-1\right)}{1}-\sqrt{3}-\sqrt{2}\)
\(=2+\sqrt{3}+2-\sqrt{2}-\sqrt{3}-\sqrt{2}\)
\(=4-2\sqrt{2}\)
b: \(N=\left(1-\dfrac{\sqrt{5}\left(\sqrt{5}+1\right)}{\sqrt{5}+1}\right)\left(\dfrac{-\sqrt{5}\left(1-\sqrt{5}\right)}{1-\sqrt{5}}-1\right)\)
\(=\left(1-\sqrt{5}\right)\left(-\sqrt{5}-1\right)\)
\(=\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)=5-1=4\)
a) \(P=\dfrac{3+2\sqrt{3}}{\sqrt{3}}+\dfrac{2+\sqrt{2}}{\sqrt{2}+1}-\left(\sqrt{2}+\sqrt{3}\right)\)
\(P=\dfrac{\sqrt{3}\cdot\left(\sqrt{3}+2\right)}{\sqrt{3}}+\dfrac{\sqrt{2}\cdot\left(\sqrt{2}+1\right)}{\sqrt{2}+1}-\sqrt{2}-\sqrt{3}\)
\(P=\sqrt{3}+2+\sqrt{2}-\sqrt{2}-\sqrt{3}\)
\(P=2\)
b) \(N=\left(1-\dfrac{5+\sqrt{5}}{1+\sqrt{5}}\right)\left(\dfrac{5-\sqrt{5}}{1-\sqrt{5}}-1\right)\)
\(N=\left[1-\dfrac{\sqrt{5}\left(1+\sqrt{5}\right)}{1+\sqrt{5}}\right]\left[1+\dfrac{\sqrt{5}\left(1-\sqrt{5}\right)}{1-\sqrt{5}}\right]\)
\(N=\left(1-\sqrt{5}\right)\left(1+\sqrt{5}\right)\)
\(N=1^2-\left(\sqrt{5}\right)^2\)
\(N=-4\)
c) \(Q=\left(\dfrac{5+2\sqrt{5}}{2-\sqrt{5}}-2\right)\left(\dfrac{5+3\sqrt{5}}{3+\sqrt{5}}-2\right)\)
\(Q=\left[\dfrac{\sqrt{5}\left(\sqrt{5}-2\right)}{\sqrt{5}-2}+2\right]\left[\dfrac{\sqrt{5}\left(\sqrt{5}+3\right)}{\sqrt{5}+3}-2\right]\)
\(Q=\left(\sqrt{5}+2\right)\left(\sqrt{5}-2\right)\)
\(Q=\left(\sqrt{5}\right)^2-2^2\)
\(Q=1\)
Bài 1
a, Tính P=1+1/2(1+2)+1/3(1+2+3)+1/4(1+2+3+4)+....+1/2012(1+2+3+...+2012)
b,Tìm x thỏa mãn 4^5+4^5+4^5+4^5/3^5+3^5+3^5.6^5+6^5+6^5+6^5+6^5+6^5/2^5+2^5=2^x
Kho..................wa.....................troi.....................thi......................lanh.................ret.......................ai........................tich..........................ung.....................ho........................minh.....................cho....................do....................lanh
Kho..................wa.....................troi.....................thi......................lanh.................ret.......................ai........................tich..........................ung.....................ho........................minh.....................cho....................do....................lanh
A=2 mũ 3 + 2 mũ 4 + 2 mũ 5 + 2 mũ 6 + 2 mũ 7 +.....+ 2 mũ 90
B=1+5+5 mũ 2 + 5 mũ 3 +5 mũ 4 +......+5 mũ 50
C=1/5 +1/5 mũ 2 + 1/5 mũ 3 + 1/5 mũ 4 +1/5 mũ 6 +......+1/5 mũ 102
D=1/5 +1/5 mũ 3 + 1/5 mũ 4 +1/5 mũ 5 + 1/5 mũ 6 +1/5 mũ 105
A = 2^3 + 2^4+ 2^5+ 2^6 + 2^7 + ... + 2^90
2A = 2^4 + 2^5 + 2^6 + 2^7 + 2^8 + .... + 2^90 + 2^100
2A - A = ( 2^4 + 2^5 + 2^6 + 2^7 + 2^8 + .... + 2^90 + 2^100 ) - ( 2^3 + 2^4+ 2^5+ 2^6 + 2^7 + ... + 2^90 )
A = 2^100 - 2^3
B = 1 + 5 + 5^2 + 5^3 + 5^4 + .... + 5^50
5B = 5 + 5^2 + 5^3 + 5^4 + 5^5 + .... + 5^50 + 5^51
5B - B = ( 5 + 5^2 + 5^3 + 5^4 + 5^5 + .... + 5^50 + 5^51 ) - ( 1 + 5 + 5^2 + 5^3 + 5^4 + .... + 5^50 )
4B = 5^51 - 1
B = 5^51 - 1 / 4
a,1/3 .(x-2/5)=3/4 b, 7/3:(x-2/3)=4/5 c,1/3.(x-2/5)=4/5 d, 2/3.(x-1/2)-1/4.(x-2/5)=7/3 e,3/7 .(x-2/3)+1/2=5/4.(x-2) f,1/2.(x-3)+1/3.(x-4)+1/4.(x-5)=1/5 g,[2/3.(x-1/2)-4/5]:(x-1/3)=21/5 h, {x-[1/2.(x-3)+11/5]}:(x-1/2)=3/5 i,x.(x-2/5)-(x+2).x+11/4=4/3
a: =>x-2/5=3/4:1/3=3/4*3=9/4
=>x=9/4+2/5=45/20+8/20=53/20
b: =>x-2/3=7/3:4/5=7/3*5/4=35/12
=>x=35/12+2/3=43/12
c: 1/3(x-2/5)=4/5
=>x-2/5=4/5*3=12/5
=>x=12/5+2/5=14/5
d: =>2/3x-1/3-1/4x+1/10=7/3
=>5/12x-7/30=7/3
=>5/12x=7/3+7/30=77/30
=>x=77/30:5/12=154/25
e: \(\Leftrightarrow x\cdot\dfrac{3}{7}-\dfrac{2}{7}+\dfrac{1}{2}-\dfrac{5}{4}x+\dfrac{5}{2}=0\)
=>\(x\cdot\dfrac{-23}{28}=\dfrac{2}{7}-3=\dfrac{-19}{7}\)
=>x=19/7:23/28=76/23
f: =>1/2x-3/2+1/3x-4/3+1/4x-5/4=1/5
=>13/12x=1/5+3/2+4/3+5/4=257/60
=>x=257/65
i: =>x^2-2/5x-x^2-2x+11/4=4/3
=>-12/5x=4/3-11/4=-17/12
=>x=17/12:12/5=85/144
>, < , = ?
5 – 2 … 4 | 5 – 4 … 2 | 4 + 1 … 5 |
5 – 2 …. 3 | 5 – 3 … 1 | 5 – 1 … 5 |
5 – 2 … 2 | 5 – 1 …. 4 | 5 – 4 … 0 |
Lời giải chi tiết:
5 – 2 < 4 | 5 – 4 < 2 | 4 + 1 = 5 |
5 – 2 = 3 | 5 – 3 > 1 | 5 – 1 < 5 |
5 – 2 > 2 | 5 – 1 = 4 | 5 – 4 > 0 |
5-2<4 5-4<2 4+1=5
5-2=3 5-3>1 5-1<5
5-2>2 5-1=4 5-4>0
Tính:
5 – 2 – 1 = … | 4 – 2 – 1 = … | 3 – 1 – 1 = …. |
5 – 2 – 2 = … | 5 – 1 – 2 = … | 5 – 1 – 1 = …. |
Lời giải chi tiết:
5 – 2 – 1 = 2 | 4 – 2 – 1 = 1 | 3 – 1 – 1 = 1 |
5 – 2 – 2 = 1 | 5 – 1 – 2 = 2 | 5 – 1 – 1 = 3 |
a)(5+1/5-2/9)-(2-1/23-3/35+5/6)-(8+2/7-1/18)
b) 1/3-3/4(-3/5+1/64- -2/9-1/36+1/15
c) -5/7-(-5/67)+13/10+1/2+(-1/6)+1 3/14-(-2/5)
d)3/5:(-1/15-1/6)+3/5:(-1/3-1 1/15)
>, <, = ?
4…5 | 1…4 | 2…3 | 1…1 |
2…2 | 5…2 | 2…4 | 5…1 |
3…1 | 3…3 | 2…5 | 3…5 |
Lời giải chi tiết:
4 < 5 | 1 < 4 | 2 < 3 | 1 = 1 |
2 = 2 | 5 > 2 | 2 < 4 | 5 > 1 |
3 > 1 | 3 = 3 | 2 < 5 | 3 < 5 |
>, <, = ?
2 + 2 … 5 | 2 + 1 … 1 + 2 | 3 + 1 … 3 + 2 |
2 + 3 … 5 | 2 + 2 …1 + 2 | 3 + 1 … 1 + 3 |
5 + 0 … 5 | 2 + 0 …1 + 2 | 1 + 4 …. 4 + 1 |
Lời giải chi tiết:
2 + 2 < 5 | 2 + 1 = 1 + 2 | 3 + 1 < 3 + 2 |
2 + 3 = 5 | 2 + 2 > 1 + 2 | 3 + 1 = 1 + 3 |
5 + 0 = 5 | 2 + 0 < 1 + 2 | 1 + 4 = 4 + 1 |
2 + 2 < 5 2 + 1 = 1 + 2 3 + 1 < 3 + 2
2 + 3 = 5 2 + 2 > 1 + 2 3 + 1 = 1 + 3
5 + 0 = 5 2 + 0 < 1 + 2 1 + 4 = 4 + 1