A = (5^56 + 5^7) : (5^49 + 1)

A = 5^7.(5^49 + 1) : (5^49 + 1)

A = 5^7.[(5^49 + 1) : (5^49 + 1)]

A = 5^7.1

A = 5^7

(7^22 + 7^21 + 7^20) : (2^5 + 2^4 + 3^2)

= 7^20.(7^2 + 7 + 1) : (2^5 + 2^4 + 3^2)

= 7^20.(49 + 1 + 7) : (32 + 16 + 9)

= 7^20.(50 + 7) : (48 + 9)

= 7^20.57: 57

= 7^20.(57:57)

= 7^20.1

=7^20

a, Ta có: \(A=\left|x+2\right|+\left|9-x\right|\ge\left|X+2+9-x\right|=11\)

Dấu "=' xảy ra khi \(\left(x+2\right)\left(9-x\right)\ge0\Leftrightarrow-2\le x\le9\)

Vậy Min_A = 11 khi -2 =< x =< 9

b, Vì \(\left(x-1\right)^2\ge0\Rightarrow-\left(x-1\right)^2\le0\Rightarrow B=\frac{3}{4}-\left(x-1\right)^2\le\frac{3}{4}\)

Dấu "=" xảy ra khi x = 1

Vậy Max_B = 3/4 khi x=1

Ta có :\(A=\left|x+2\right|+\left|9-x\right|\ge\left|x+2+9-x\right|=11\)

Vậy \(A_{min}=11\) khi \(2\le x\le9\)

a, x> -5

b, x>1

nhầm b, x> 0

a) Ta có: \(\left|2x-\dfrac{1}{3}\right|\ge0\forall x\)

\(\Leftrightarrow\left|2x-\dfrac{1}{3}\right|-\dfrac{7}{4}\ge-\dfrac{7}{4}\forall x\)

Dấu '=' xảy ra khi \(2x=\dfrac{1}{3}\)

hay \(x=\dfrac{1}{6}\)

Vậy: \(A_{min}=-\dfrac{7}{4}\) khi \(x=\dfrac{1}{6}\)

b) Ta có: \(\dfrac{1}{3}\left|x-2\right|\ge0\forall x\)

\(\left|3-\dfrac{1}{2}y\right|\ge0\forall y\)

Do đó: \(\dfrac{1}{3}\left|x-2\right|+\left|3-\dfrac{1}{2}y\right|\ge0\forall x,y\)

\(\Leftrightarrow\dfrac{1}{3}\left|x-2\right|+\left|3-\dfrac{1}{2}y\right|+4\ge4\forall x,y\)

Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}x-2=0\\3-\dfrac{1}{2}y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=6\end{matrix}\right.\)

Vậy: \(B_{min}=4\) khi x=2 và y=6

Tính giá trị của biểu thức

a) 25,6 + 27,5×2,6 = 25,6 + 71,5 = 97,1

b) (25,6 + 27,5) ×2,6= 53,1 x 2,6 = 138,06

a)\(97,1\)

b)\(138,06\)

1 C

2 A

3 C

4 D

5 B

II

1 C

2 A

3 B

4 C

5 D

\(-9x^2+12x-15=\left(-11\right)-\left(9x^2-12x+4\right)=\left(-11\right)-\left(3x-2\right)^2\le-11< 0\)

\(-5-\left(x-1\right).\left(x+2\right)=-5-\left(x^2+x-2\right)=-\left(x^2+x+3\right)=-\left(\left(x+\frac{1}{2}\right)^2+\frac{11}{4}\right)\le-\frac{11}{4}< 0\)

1 B

2 A

3 D

4 C

5 C

6 A

7 B

8 D