A = 1 x 2 + 2 x 3 + 3 x 4 + 4 x 5 + ... + 99 x 100

A = 2 + 6 + 12 + 20 + ... 9900

A = [2+9900]   rồi bn nhân tổng số từ số 2 - 9900

\(3A=1.2.3+2.3.\left(4-1\right)+...+99.100.\left(101-98\right)\)

\(3A=1.2.3+2.3.4-1.2.3+...+99.100.101-98.99.100\)

\(3A=99.100.101\)

\(\Rightarrow A=\frac{99.100.101}{3}\)

5(x-1)=125-25

5(x-1)=100

x-1=100:5

x-1=20

x=20+1

x=21

12(x-1):3=64+8

12(x-1):3=72

12(x-1)=72.3

12(x-1)=216

x-1=216:12

x-1=18

x=18+1

x=19

(x-1)^3=5^3

=>x-1=5

x=5+1

x=6

\(4^{x+3}+4^{x+2}+4^{x+1}+4^x=5440\)

\(\Rightarrow4^x.4^3+4^x.4^2+4^x.4+4^x=5440\)

\(\Rightarrow4^x\left(4^3+4^2+4+1\right)=5440\)

\(\Rightarrow4^x.\left(64+16+4+1\right)=5440\)

\(\Rightarrow4^x.85=5440\)

\(\Rightarrow4^x=5440:85\)

\(\Rightarrow4^x=64=4^3\)

\(\Rightarrow x=3\)

`5/2 -3(1/3-x)=1/4-7x`

`=> 5/2 - 1 + 3x=1/4 -7x`

`=>3x+7x= 1/4 - 5/2 +1`

`=> 10x= 1/4 - 10/4 +4/4`

`=>10x= -5/4`

`=>x=-5/4 :10`

`=>x=-5/4 xx1/10`

`=>x= -5/40=-1/8`

=>5/2-3+3x=1/4-7x

=>10x=1/4-5/2+3=3/4

=>x=3/40

`x/2+x+x/3+x+x+x/4=5 3/4`

`=>3x+x/2+x/3+x/4=23/4`

`=>49/12x=23/4`

`=>x=69/49`

Vậy `x=69/49`

giúp mik với xin các bạn đó mik đnag cần gấp

Soạn đề bằng thanh công cụ cho rõ nha bạn

Ta có : 1³+ 2³+...+100³ = (1+2+3+...+100)²  

Đặt A = 1+2+3+...+100

⇒A= \(\dfrac{\left(100+1\right).100}{2}\) ⇔A= 5050

⇒5050² = (x-1)² ⇔ x=5051

\(a,\Leftrightarrow\left(5x+1\right)\left(x-4\right)-\left(x-4\right)=0\\ \Leftrightarrow\left(x-4\right)\left(5x+1-x\right)=0\\ \Leftrightarrow5x\left(x-4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\end{matrix}\right.\\ b,\Leftrightarrow2x^2-10x-2x^2-3x=26\\ \Leftrightarrow-13x=26\\ \Leftrightarrow x=-2\\ c,\Leftrightarrow x^3+1-x^3+3x=15\\ \Leftrightarrow3x=14\\ \Leftrightarrow x=\dfrac{14}{3}\)

\(d,\Leftrightarrow x^3-5x+2x^2-10+5x-2x^2-17=0\\ \Leftrightarrow x^3-27=0\\ \Leftrightarrow x^3=27\\ \Leftrightarrow x=3\)