Chương I : Số hữu tỉ. Số thực

a) Ta thấy: \(40< 50\) và đây là 2 phân số có tử số nhỏ hơn mẫu số nên:

\(\Rightarrow\left(\dfrac{1}{2}\right)^{40}< \left(\dfrac{1}{2}\right)^{50}\)

b) Ta có:

\(243^3=\left(3^5\right)^3=3^{15}\)

\(125^5=\left(5^3\right)^5=5^{15}\)

Mà: \(3^{15}< 5^{15}\)

\(\Rightarrow243^3< 125^5\)

Để (x + 1)/(2x + 1) ∈ Z thì (x + 1) ⋮ (2x + 1)

⇒ 2(x + 1) ⋮ (2x + 1)

⇒ (2x + 2) ⋮ (2x + 1)

⇒ (2x + 1 + 1) ⋮ (2x + 1)

Để 2(x + 1) ⋮ (2x + 1) thì 1 (2x + 1)

⇒ 2x + 1 ∈ Ư(1)

⇒ 2x + 1 ∈ {-1; 1}

⇒ 2x ∈ {-2; 0}

⇒ x ∈ {-1; 0}

`@` `\text {Ans}`

`\downarrow`

`1)`

`5/7*37 13/23 - 51 13/23*5/7`

`= 5/7* (37 13/23 - 51 13/23)`

`= 5/7* (-14)`

`= -10`

`2)`

`-2/3 +1/3+0,5+2 1/2`

`= -2/3 + 1/3 + 1/2 + 5/2`

`= (-2/3+1/3) + (1/2+5/2)`

`= -1/3 + 3`

`=8/3`

`3)`

`-0,5+2/3+1/2`

`= -1/2 + 2/3 + 1/2`

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

`= 2/3`

`4)`

`(8+2 1/3-3/5) -(5+0,4)-(3 1/2 -2)`

`= 8+ 7/3 - 3/5 - 5 - 0,4 - 7/2 + 2`

`= (8+2-5) + (-3/5 - 2/5) + (7/3 - 7/2)`

`= 5 - 1 - 7/6`

`= 4 - 7/6 = 17/6`

`5)`

`(2/9-7/12):3/4+(16/9-5/12):3/4`

`= (2/9 - 7/12) \times 4/3 + (16/9 - 5/12) \times 4/3`

`= 4/3 *(2/9 - 7/12 + 16/9 - 5/12)`

`= 4/3 * [(2/9 + 16/9) + (-7/12 - 5/12)]`

`= 4/3 * ( 2 - 1)`

`= 4/3 * 1 = 4/3`

`6)`

`-(2021.0,7+19,75) +0,7- (8-19,75)`

`= -2021*0,7 -19,75 + 0,7 - 8 + 19,75`

`= 0,7*(-2021 + 1) - 8`

`= -1414-8`

`= -1422`

`7)`

`15/34+7/21+19/34-20/15`

`= (15/34 + 19/34) + 7/21 - 20/15`

`= 1 + 7/21 - 20/15`

`= 4/3 - 20/15 =0`

`8)`

`2 5/6+1/6:(-5/8)`

`= 17/6 + (-4/15)`

`= 77/30`

`9)`

`(-2)^2 +2/9. (4/5-2/3)`

`= 4 + 2/9*2/15`

`= 4+4/135`

`= 544/135`

`10)`

`(-1/5+3/7):5/4+(-4/5+4/7):5/4`

`= (-1/5+3/7) * 4/5 + (-4/5+4/7) * 4/5`

`= 4/5*(-1/5 +3/7-4/5+4/7)`

`= 4/5*[(-1/5-4/5)+(3/7+4/7)]`

`= 4/5* (-1+1)`

`= 4/5*0=0`

`11)`

`2022,2021 . 1954,1945+ 2022,2021 . (-1954,1945)`

`= 2022,2021 * [1954,1945 + (-1954,1945)]`

`= 2022,2021*0 `

`= 0`

`12)`

`-5,2 .72 +69,1 +5,2 . (-28)+(-1,1)`

`= -5,2*72 + 69,1 - 5,2*28 - 1,1`

`= -5,2*(72+28) + (69,1 - 1,1)`

`= -5,2*100 + 68`

`= -520 + 68`

`= -452`

`13)`

`(7 -1/2-3/4) : (5-1/4-5/8)`

`= 23/4 \div 33/8`

`=46/33`

`14)`

`(8+ 2 1/3 -3/5) -(5+0,4) -( 3 1/3 - 2)`

`= 8+ 2 1/3 - 3/5 - 5 - 0,4 - 3 1/3 + 2`

`= (8+2-5) + (2 1/3 - 3 1/3) - (0,6 + 0,4) `

`= 5 - 1 - 1`

`= 3`

help lười tính quá

2: \(=\dfrac{-1}{3}+3=\dfrac{8}{3}\)

3: =1/2-1/2+2/3=2/3

5: \(=\dfrac{4}{3}\left(\dfrac{2}{9}-\dfrac{7}{12}+\dfrac{16}{9}-\dfrac{5}{12}\right)=\dfrac{4}{3}\)

12: \(=5.2\left(-72-28\right)+68=-520+68=-452\)

13: \(\dfrac{23}{4}:\dfrac{33}{8}=\dfrac{46}{33}\)

6:

a: \(A\left(x\right)=-x^4+x^3+2x^2-x-3\)

\(B\left(x\right)=x^3+3x^2-2x+12\)

b: C(x)=A(x)+B(x)

=-x^4+x^3+2x^2-x-3+x^3+3x^2-2x+12

=-x^4+2x^3+5x^2-3x+9

C(x)=A(x)-B(x)

=-x^4+x^3+2x^2-x-3-x^3-3x^2+2x-12

=-x^4-x^2+x-15

Cái (a,b)=1 có nghĩa là ƯCLN(a,b)=1 nha bạn

Tương tự với hai cái còn lại

Do \(x^2+y^2+z^2=1\Rightarrow x^2< 1\Rightarrow x< 1\)

\(\Rightarrow x^5< x^2\)

Tương tự ta có: \(y< 1\Rightarrow y^6< y^2\); \(z< 1\Rightarrow z^7< z^2\)

\(\Rightarrow x^5+y^6+z^7< x^2+y^2+z^2\)

\(\Rightarrow x^5+y^6+z^7< 1\)

\(\dfrac{a}{b}=\dfrac{c}{d}\Rightarrow\dfrac{a}{c}=\dfrac{b}{d}\)

Áp dụng t/c của DTSBN , ta có :

\(\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{2a+b}{2c+d}=\dfrac{3a-b}{3c-d}\\ \Rightarrow\dfrac{2a+b}{2c+d}=\dfrac{3a-b}{3c-d}\\ \Rightarrow\dfrac{2a+b}{3a-b}=\dfrac{2a+d}{3c-a}\left(đpcm\right)\)