Bài 2

a: a(b-2)+b

=ab-2a+b

=3-5

=-2

b: \(4a^2+b^2=4a^2-4ab+b^2+4ab\)

\(=\left(2a-b\right)^2+4ab=5^2+4\cdot3\)

=25+12

=37

Bài 1:

b: \(a^2+b^2=\left(a+b\right)^2-2ab=5^2-2\cdot\left(-6\right)=25+12=37\)

c: \(a^4+b^4=\left(a^2+b^2\right)^2-2a^2b^2\)

\(=37^2-2\cdot\left(ab\right)^2=37^2-2\cdot\left(-6\right)^2=37^2-2\cdot36=1297\)

a) A = 1                          b) B = -2.

giả sử A>B

\(\Leftrightarrow\dfrac{a}{2a+1}>\dfrac{3x+1}{6x+3}\)

\(\Leftrightarrow\dfrac{3a}{3\left(2x+1\right)}>\dfrac{3x+1}{6x+3}\)

\(\Leftrightarrow\dfrac{3a}{6a+3}>\dfrac{3x+1}{6x+3}\)

\(\Leftrightarrow3a>3a+1\)

\(\Leftrightarrow0>1\) ( vô lí )

vậy \(\Rightarrow B>A\)

giả sử A>B

( vô lí )

vậy

Ta có: \(\left(\frac{a+b}{b}-\frac{2b}{b-a}\right)\cdot\frac{b-a}{a^2+b^2}+\left(\frac{a^2+1}{2a-1}-\frac{a}{2}\right):\frac{a+2}{1-2a}\)

\(=\frac{\left(a+b\right)\left(a-b\right)+2b^2}{b\left(a-b\right)}\cdot\frac{-\left(a-b\right)}{a^2+b^2}+\frac{2\left(a^2+1\right)-a\cdot\left(2a-1\right)}{2\left(2a-1\right)}\cdot\frac{-\left(2a-1\right)}{a+2}\)

\(=\frac{a^2-b^2+2b^2}{-b}\cdot\frac{1}{a^2+b^2}+\frac{2a^2+2-2a^2+a}{2}\cdot\frac{-1}{a+2}\)

\(=\frac{-1}{b}+\frac{-1}{2}=\frac{-2-b}{2b}\)

Ta có: \(A-B\)

\(=1011\left(1+\frac13+\frac15+\cdots+\frac{1}{2019}\right)-1010\left(\frac12+\frac14+\cdots+\frac{1}{2020}\right)\)

\(=1010\left(1-\frac12+\frac13-\frac14+\cdots+\frac{1}{2019}-\frac{1}{2020}\right)+\left(1+\frac13+\cdots+\frac{1}{2019}\right)\)

Vì \(1-\frac12>0;\frac13-\frac14>0;\ldots;\frac{1}{2019}-\frac{1}{2020}>0\)

nên \(1-\frac12+\frac13-\frac14+\cdots+\frac{1}{2019}-\frac{1}{2020}>0\)

=>\(1010\left(1-\frac12+\frac13-\frac14+\cdots+\frac{1}{2019}-\frac{1}{2020}\right)>0\)

=>A-B>0

=>A>B

a) Ta có: \(\dfrac{m^2+2m+1}{m^2-1}\)

\(=\dfrac{\left(m+1\right)^2}{\left(m+1\right)\left(m-1\right)}\)

\(=\dfrac{m+1}{m-1}\)

b) Ta có: \(\dfrac{2a^4+3a^3+2a+3}{\left(a^2-a+1\right)\left(4a+6\right)}\)

\(=\dfrac{a^3\left(2a+3\right)+\left(2a+3\right)}{\left(a^2-a+1\right)\left(4a+6\right)}\)

\(=\dfrac{\left(2a+1\right)\left(a+1\right)\left(a^2-a+1\right)}{2\left(a^2-a+1\right)\left(2a+3\right)}\)

\(=\dfrac{a+1}{2}\)

MN K BT?

1.

a. -3a - 1 + 1 > -3b - 1 + 1 (cộng cả 2 vế cho 1)

  -3a . \(\left(\dfrac{-1}{3}\right)\) <  -3b . \(\left(\dfrac{-1}{3}\right)\) (nhân cả vế cho \(\dfrac{-1}{3}\) )

         a < b

b. 4a + 3 + (- 3) < 4b + 3 +(- 3) (cộng cả 2 vế cho -3)

   4a . \(\dfrac{1}{4}\) < 4b . \(\dfrac{1}{4}\) (nhân cả 2 vế cho \(\dfrac{1}{4}\) )

        a < b

2. 

a. Ta có: a < b 

3a < 3b ( nhân cả 2 vế cho 3)

3a - 7 < 3b - 7 (cộng cả 2 vế cho - 7 )

b. Ta có: a < b

-2a > -2b (nhân cả 2 vế cho -2)

5 - 2a > 5 - 2b ( cộng cẩ 2 vế cho 5)

c. Ta có: a < b 

2a < 2b (nhân cả vế cho 2)

2a + 3 < 2b + 3 (cộng cả 2 vế cho 3)

d. Ta có: a < b

3a < 3b (nhân cả 2 vế cho 3)

3a - 4 < 3b - 4 (cộng cả 2 vế cho -4)

Ta có: 3 < 4

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