ai làm cung dúng

cách trên gọn hơn cách dưới

hai lời giải như nhau mà

làm thế nào mà chẳng được

bố bạn làm đúng đấy vì bước x=1/10+3/5 bạn đổi ra sẽ làm dễ và chình xác hơn. Chúc bạn học tốt

1) 3/9 + 5/9 = 8/9

2) 1/2 x 2/3 x 3/4 x 4/5

= 1/5

(1-1/2)×(1-1/3)×(1-1/4)×(1-1/5)×1-1/6=1/2×2/3×3/4×4/5×5/6=1/6

\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x.\left(x+1\right):2}=\frac{399}{400}\)

\(2.\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{399}{400}\)

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x.\left(x+1\right)}=\frac{399}{400}:2\)

\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{399}{400}.\frac{1}{2}\)

\(\frac{1}{2}-\frac{1}{x+1}=\frac{399}{800}\)

\(\frac{1}{x+1}=\frac{1}{2}-\frac{399}{800}\)

\(\frac{1}{x+1}=\frac{400}{800}-\frac{399}{800}\)

\(\frac{1}{x+1}=\frac{1}{800}\)

\(=>x+1=800\)

\(=>x=800-1=799\)

Vậy x = 799

Ủng hộ mk nha ^_-

ok cảm ơn nha

\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right):2}=\frac{399}{400}\)

\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{399}{400}\)

\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{399}{400}\)

\(2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{399}{400}\)

\(2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{399}{400}\)

\(2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{399}{400}\)

\(\frac{1}{2}-\frac{1}{x+1}=\frac{399}{200}\)

\(\frac{1}{x+1}=\frac{-299}{200}\)

\(x+1=\frac{-200}{299}\)

\(x=\frac{-499}{299}\)

1, x³+ 6x²+11x+6

= x³ + 2x² + 4x² + 8x + 3x + 6 

= x²(x + 2) + 4x(x + 2) + 3(x + 2)

= (x + 2)(x² + 4x + 3)

2, x⁴+3x³-7x²-27x-18

= x⁴ + 3x³ - 9x² + 2x² - 27x -18

= (x⁴ - 9x²) + (3x³ - 27x) + (2x² - 18)

= x²(x² - 9) + 3x(x² - 9) + 2(x² - 9)

= (x² - 9)(x² + 3x + 2)

= (x + 3)(x - 3)(x² + 3x + 2)

3, x³-8x²+x+42

= x³ - 7x² - x² + 7x - 6x + 42

= (x³ - 7x²) - (x² - 7x) - (6x - 42)

= x²(x - 7) - x(x - 7) - 6(x - 7)

= (x - 7)(x² - x - 6) 

4, x⁴+5x³-7x²-41x-30 

= x⁴ + x³ + 4x³ - 4x² - 11x² - 11x - 30x - 30

= (x⁴ + x³) + (4x³ - 4x²) - (11x² + 11x) - (30x + 30)

= x³(x + 1) + 4x²(x + 1) - 11x(x + 1) - 30(x + 1)

= (x³ + 4x² - 11x - 30)(x + 1)

5, x⁵+x-1

= x⁵ - x⁴ + x³ + x⁴ - x³ + x² - x²+ x -1 

= x³(x² - x + 1)+ x²(x² - x + 1)- (x² - x + 1) 

= (x² - x + 1)(x³ + x² - 1)

6, x⁵-x⁴-1

= x⁵ - x³ - x² - x⁴ + x² + x + x³ - x - 1 

= x²(x³ - x - 1) - x(x³ - x - 1) + (x³ - x - 1)

= (x² - x + 1)(x³ - x - 1)

1, x 3+ 6x 2+11x+6

= x 3 + 2x 2 + 4x 2 + 8x + 3x + 6

= x 2 ﴾x + 2﴿ + 4x﴾x + 2﴿ + 3﴾x + 2﴿

= ﴾x + 2﴿﴾x 2 + 4x + 3﴿

2, x 4+3x 3‐7x 2‐27x‐18

= x 4 + 3x 3 ‐ 9x 2 + 2x 2 ‐ 27x ‐18

= ﴾x 4 ‐ 9x 2 ﴿ + ﴾3x 3 ‐ 27x﴿ + ﴾2x 2 ‐ 18﴿

= x 2 ﴾x 2 ‐ 9﴿ + 3x﴾x 2 ‐ 9﴿ + 2﴾x 2 ‐ 9﴿

= ﴾x 2 ‐ 9﴿﴾x 2 + 3x + 2﴿

=﴾x + 3﴿﴾x ‐ 3﴿﴾x 2 + 3x + 2﴿

3, x 3‐8x 2+x+42

= x 3 ‐ 7x 2 ‐ x 2 + 7x ‐ 6x + 42

= ﴾x 3 ‐ 7x 2 ﴿ ‐ ﴾x 2 ‐ 7x﴿ ‐ ﴾6x ‐ 42﴿

= x 2 ﴾x ‐ 7﴿ ‐ x﴾x ‐ 7﴿ ‐ 6﴾x ‐ 7﴿

= ﴾x ‐ 7﴿﴾x 2 ‐ x ‐ 6﴿

4, x 4+5x 3‐7x 2‐41x‐30

= x 4 + x 3 + 4x 3 ‐ 4x 2 ‐ 11x 2 ‐ 11x ‐ 30x ‐ 30

= ﴾x 4 + x 3 ﴿ + ﴾4x 3 ‐ 4x 2 ﴿ ‐ ﴾11x 2 + 11x﴿ ‐ ﴾30x + 30﴿

= x 3 ﴾x + 1﴿ + 4x 2 ﴾x + 1﴿ ‐ 11x﴾x + 1﴿ ‐ 30﴾x + 1﴿

= ﴾x 3 + 4x 2 ‐ 11x ‐ 30﴿﴾x + 1﴿

5, x 5+x‐1

= x 5 ‐ x 4 + x 3 + x 4 ‐ x 3 + x 2 ‐ x 2+ x ‐1

= x 3 ﴾x 2 ‐ x + 1﴿+ x 2 ﴾x 2 ‐ x + 1﴿‐ ﴾x 2 ‐ x + 1﴿

= ﴾x 2 ‐ x + 1﴿﴾x 3 + x 2 ‐ 1﴿ 6, x 5‐x 4‐1

= x 5 ‐ x 3 ‐ x 2 ‐ x 4 + x 2 + x + x 3 ‐ x ‐ 1

= x 2 ﴾x 3 ‐ x ‐ 1﴿ ‐ x﴾x 3 ‐ x ‐ 1﴿ + ﴾x 3 ‐ x ‐ 1﴿

= ﴾x 2 ‐ x + 1﴿﴾x 3 ‐ x ‐ 1﴿ 

Ta có : \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+.....+\frac{1}{x\left(x+1\right):2}=\frac{399}{400}\)

\(\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+.....+\frac{2}{x\left(x+1\right)}=\frac{399}{400}\left(\text{​Quy đồng nhé !}\right)\)

\(\Leftrightarrow\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+......+\frac{2}{x\left(x+1\right)}=\frac{399}{400}\)

\(\Leftrightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+......+\frac{1}{x\left(x+1\right)}\right)=\frac{399}{400}\)

\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{2}+\frac{1}{3}-\frac{1}{3}+.....+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{399}{400}\)

\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{399}{400}\)

\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{399}{800}\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{399}{800}\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{800}\)

=> x + 1 = 800 

<=> x = 799

1/3+1/6+1/10+...+1/x(x+1):2=399/400

2.[1/3.2+1/6.2+1/10.2+...+1/x(x+1)]=399/400

2.[1/6+1/12+1/20+...+1/x(x+1)]=399/400

2.[1/2.3+1/3.4+1/4.5+...+1/x(x+1)]=399/400

1/2-1/3+1/3-1/4+1/4-1/5+...+1/x-1/x+1=399/800

1/2-1/x+1=399/800

1/x+1=1/800

=> x+1=800

=> x=799

c,Dãy trên có số số hạng là:

(52-2):2+1=26 số hạng

Tổng của dãy trên là:

(52+2).26:2=702

Đáp số :.....

\(\frac{1}{2}\times\frac{1}{3}+\frac{1}{2}\times\frac{2}{3}-\frac{2}{4}\)

\(\frac{1}{2}\times\frac{1}{3}+\frac{1}{2}\times\frac{2}{3}-\frac{1}{2}\)

\(\frac{1}{2}\left(\frac{1}{3}+\frac{2}{3}-1\right)\)

\(\frac{1}{2}.0\)

\(=0\)

1/2x1/3+1/2x2/3-2/4

=1/2x1/3+1/2x2/3-1/2x1

=1/2x(1/3+2/3-1)

=1/2x0

=0

2+4+6+....+52

Số số hạng là 

(52-2):2+1=26(số hạng)

Tổng là 

(50+2)x26:2=676

Đáp số :...