Giup minh voi cau nay voi:
a,1x2x3x4/x5x6x7x8
b,23+23x2+23x3+23x4
c,2x1/2x3x1/3x4x1/4x5x1/5
d,248x2005-205x148
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Bài 1: Tính
a, 1/2 x 2/3 x 3/4 = 1/4
b, 7/8 x 8/9 x 9/10 = 7/10
c, 5/14 x 7/15 x 28/7 = 2/3
d, 2 x 1/2 x 3 x 1/3 x 4 x 1/4 x 5 x 1/5 = 1
Bài 2: Tính
a, 7/20 - ( 5/8 - 3/5 ) = 7/20 - 1/40 = 14/40 - 1/40 = 13/40
b, 5/6 + ( 5/9 - 1/4 ) = 5/6 + 11/36 = 30/36 + 11/36 = 41/36
c, 9/10 - ( 2/5 + 3/10 ) + 7/20 = 9/10 - 7/10 + 7/20 = 2/10 + 7/20 = 4/20 + 7/20 = 11/20.
Bài 3: Tìm x:
a, 1/2 + x = 5/6
x = 5/6 - 1/2
x = 1/3
b, 5/6 - x = 1/3
x = 5/6 - 1/3
x = 1/2
c, x - 1/mấy vậy bạn
d, 1/3 x x = 1/6
x = 1/6 : 1/3
x = 1/2
1/
25x12x30x4
= (25x4)x(12x30)
=100x3600
=360 000
2/
23+23x2+23x3+23x4
=23x1+23x2+23x3+23x4
=23x(1+2+3+4)
=23x10
=230
3/
248x2005 - 2005x148
=(248-148)x2005
=100x2005
=200500
1/
25x12x30x4
= (25x4)x(12x30)
=100x3600
=360 000
2/
23+23x2+23x3+23x4
=23x1+23x2+23x3+23x4
=23x(1+2+3+4)
=23x10
=230
3/
248x2005 - 2005x148
=(248-148)x2005
=100x2005
=200500
Tổng 2 số: 30*2=60
Số thứ 1: 60/(4+1)*4=48
Số thứ 2: 60-48=12
Vậy St1=48, St2=12
Tổng 2 số là :
30 x 2 = 60
Ta có sơ đồ :
St1 :|___|___|___|___| tổng : 60
St2 :|___|
Tổng số phần bằng nhau là :
4 + 1 = 5 (phần)
St1 là :
60 : 5 x 4 = 48
St2 là :
60 - 48 = 12
Đ/S : st1 : 48
st2 : 12
1) \(B=\dfrac{\sqrt{x}-5}{\sqrt{x}}\)
Thay \(x=\dfrac{4}{25}\) vào B, ta được:
\(B=\dfrac{\sqrt{\dfrac{4}{25}}-5}{\sqrt{\dfrac{4}{25}}}\)
\(=\dfrac{\dfrac{2}{5}-5}{\dfrac{2}{5}}\)
\(=\dfrac{-\dfrac{23}{5}}{\dfrac{2}{5}}\)
\(=-\dfrac{23}{2}\)
2) ĐKXĐ: \(x\ne9;x\ge0\)
\(A=\dfrac{2\sqrt{x}}{\sqrt{x}-3}+\dfrac{x+9\sqrt{x}}{9-x}\)
\(=\dfrac{2\sqrt{x}}{\sqrt{x}-3}-\dfrac{x+9\sqrt{x}}{x-9}\)
\(=\dfrac{2\sqrt{x}\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}-\dfrac{x+9\sqrt{x}}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{2x+6\sqrt{x}-x-9\sqrt{x}}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{x-3\sqrt{x}}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{\sqrt{x}}{\sqrt{x}+3}\)
3) \(P=A.B\)
\(=\dfrac{\sqrt{x}}{\sqrt{x}+3}.\dfrac{\sqrt{x}-5}{\sqrt{x}}\)
\(=\dfrac{\sqrt{x}-5}{\sqrt{x}+3}\)
\(=\dfrac{\sqrt{x}+3-8}{\sqrt{x}+3}\)
\(=1-\dfrac{2}{\sqrt{x}+3}\)
Để P nhỏ nhất thì \(\dfrac{8}{\sqrt{x}+3}\) lớn nhất
Ta có:
\(\dfrac{8}{\sqrt{x}+3}\ge\dfrac{8}{3}\)
\(\Rightarrow P\) nhỏ nhất là \(1-\dfrac{8}{3}=-\dfrac{5}{3}\) khi \(x=0\)
Theo hệ thức Viet: \(\left\{{}\begin{matrix}x_1+x_2=\dfrac{3}{2}\\x_1x_2=-\dfrac{7}{2}\end{matrix}\right.\)
\(A=x_1^2+x_2^2=\left(x_1+x_2\right)^2-2x_1x_2=\dfrac{37}{4}\)
\(B=x_1^3+x_2^3=\left(x_1+x_2\right)^3-3x_1x_2\left(x_1+x_2\right)=\dfrac{153}{8}\)
\(C=x_1^4+x_2^4=\left(x_1^2+x_2^2\right)^2-2\left(x_1x_2\right)^2=\dfrac{977}{16}\)
\(D=\left|x_1-x_2\right|=\sqrt{\left(x_1-x_2\right)^2}=\sqrt{\left(x_1+x_2\right)^2-4x_1x_2}=\dfrac{\sqrt{65}}{2}\)
\(E=\left(2x_1+x_2\right)\left(2x_2+x_1\right)=2\left(x_1^2+x_2^2\right)+5x_1x_2=1\)
`3x^2+10x+3=0`
Ptr có: `\Delta'=5^2-3.3=16 > 0`
`=>` Ptr có `2` nghiệm pb
`=>` Áp dụng Viét có: `{(x_1+x_2=[-b]/a=-10/3),(x_1 .x_2=c/a=1):}`
~~~~~~~~~~~~~
`A=x_1 ^2+x_2 ^2`
`A=(x_1+x_2)^2-2x_1 .x_2`
`A=(-10/3)^2-2.1=82/9`
_______________________________________________________
`B=x_1 ^3+x_2 ^3`
`B=(x_1+x_2)(x_1 ^2-x_1 .x_2+x_2 ^2)`
`B=(x_1+x_2)[(x_1+x_2)^2 -3x_1 .x_2]`
`B=(-10/3).[(-10/3)^2-3.1]=-730/27`
_______________________________________________________
`C=x_1 ^4+x_2 ^4`
`C=(x_1 ^2+x_2 ^2)^2 -2x_1 ^2 .x_2 ^2`
`C=[(x_1+x_2)^2-2x_1 .x_2]^2-2(x_1 .x_2)^2`
`C=[(-10/3)^2-2.1]^2-2. 1^2=6562/81`
_______________________________________________________
`D=|x_1-x_2|`
`D=\sqrt{(x_1-x_2)^2}`
`D=\sqrt{(x_1+x_2)^2-4x_1.x_2}`
`D=\sqrt{(-10/3)^2-4.1}=8/3`
_______________________________________________________
`E=(2x_1+x_2)(2x_2+x_1)`
`E=4x_1 .x_2+2x_1 ^2+2x_2 ^2+x_1 .x_2`
`E=5x_1 . x_2+2(x_1+x_2)^2-4x_1 .x_2`
`E=x_1 .x_2+2(x_1+x_2)^2`
`E=1+2(-10/3)^2=209/9`
a) \(\frac{1.2.3.4}{5.6.7.8}=\frac{1.2.3.4}{5.2.3.7.2.4}=\frac{1}{70}\)
b) 23 + 23.2 + 23.3 + 23.4
23.( 1+2+3+4)
23.10
230
tinh tung cau co ma