a; 54 : 72 x 18 : 15

= 0,75 x 18 : 15

= 0,75 x 1,2

= 0,9 

b, 25 : 8 x 36 : 50

= (25  : 50) x (36 : 8)

= 0,5 x 4,5

= 2,25 

= 

a. = 0,75 x 18 : 15

    = 0,75  x 1,2

   = 0, 9

b. = ( 25 : 50 ) x ( 36 : 8)

= 0, 5 x 4,5

= 2, 25

a) \(\sqrt[4]{\dfrac{1}{16}}=\dfrac{1}{2}\)

b) \(\left(\sqrt[6]{8}\right)^2=\sqrt[\dfrac{6}{2}]{8}=\sqrt[3]{8}=2\)

c) \(\sqrt[4]{3}\cdot\sqrt[4]{27}=\sqrt[4]{3\cdot27}=\sqrt[4]{81}=3\)

Câu 5:

\(D\left(2\right)=21a+9b-6a-4b\)

\(D\left(2\right)=\left(21a-6a\right)+\left(9b-4b\right)\)

\(D\left(2\right)=15a+5b\)

Mà: \(3a+b=18\Rightarrow b=18-3b\)

\(\Rightarrow D\left(2\right)=15a+5\left(18-3b\right)\)

\(D\left(2\right)=15a+90-15a\)

\(D\left(2\right)=90\)

Vậy: ...

Câu 4:

\(D\left(1\right)=4a+10b-b+2a\)

\(D\left(1\right)=\left(4a+2a\right)+\left(10b-b\right)\)

\(D\left(1\right)=6a+9b\)

Mà: \(2a+3b=12\Rightarrow a=\dfrac{12-3b}{2}\)

\(\Rightarrow D\left(1\right)=6\left(\dfrac{12-3b}{2}\right)+9b\)

\(D\left(1\right)=\dfrac{6\left(12-3b\right)}{2}+9b\)

\(D\left(1\right)=3\left(12-3b\right)+9b\)

\(D\left(1\right)=36-9b+9b\)

\(D\left(1\right)=36\)

Vậy: ...

Câu 3:

Sửa đề: \(C=5a-4b+7a-8b\)

\(C=\left(5a+7a\right)-\left(4b+8b\right)\)

\(C=12a-12b\)

\(C=12\left(a-b\right)\)

\(C=12\cdot8\)

\(C=96\)

Vậy: ...

4:

D=6a+9b=3(2a+3b)=36

5: 

D=15a+5b=5(3a+b)=90

1: Ta có: \(P=\dfrac{x-\sqrt{x}}{x-9}+\dfrac{1}{\sqrt{x}+3}-\dfrac{1}{\sqrt{x}-3}\)

\(=\dfrac{x-\sqrt{x}+\sqrt{x}-3-\sqrt{x}-3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)

\(=\dfrac{x-\sqrt{x}-6}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)

\(=\dfrac{\left(\sqrt{x}-3\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)

\(=\dfrac{\sqrt{x}+2}{\sqrt{x}+3}\)

2)

a) Thay \(x=\dfrac{9}{4}\) vào P, ta được:

\(P=\left(\dfrac{3}{2}+2\right):\left(\dfrac{3}{2}+3\right)=\dfrac{7}{2}:\dfrac{11}{2}=\dfrac{7}{11}\)

b) Ta có: \(x=\sqrt{27+10\sqrt{2}}-\sqrt{18+8\sqrt{2}}\)

\(=5+\sqrt{2}-4-\sqrt{2}\)

=1

Thay x=1 vào P, ta được:

\(P=\dfrac{1+2}{1+3}=\dfrac{3}{4}\)

\(a,A=log_23\cdot log_34\cdot log_45\cdot log_56\cdot log_67\cdot log_78\\ =log_28\\ =log_22^3\\ =3\\ b,B=log_22\cdot log_24...log_22^n\\ =log_22\cdot log_22^2...log_22^n\\ =1\cdot2\cdot...\cdot n\\ =n!\)

1:

a: \(A=2+3\sqrt{x^2+1}>=3\cdot1+2=5\)

Dấu = xảy ra khi x=0

b: \(B=\sqrt{x+8}-7>=-7\)

Dấu = xảy ra khi x=-8

Vì x = -12 nên |x| = 12

a) 18 + |x| = 18 + 12 = 30;

b) 25 - |x| = 25 – 12 = 13;

c) |3+x| - |7| = |3 + (-12)| - 7  =  | 3+(-12)| - 7 = |-9| - 7 = 9 – 7 = 2

a: 18+|x|=18+12=30

b: 25-|x|=25-12=13

c: |3+x|-|7|=|3-12|-7=9-7=2

a) Ta có |–8| = 8; |–4| = 4.

Do đó: |–8| – |–4| = 8 – 4 = 4.

b) Ta có: |–7| = 7; |–3| = 3.

Do đó : |–7| . |–3| = 7 . 3 = 21.

c) Ta có: |18| = 18; |–6| = 6.

Do đó: |18| : |–6| = 18 : 6 = 3.

d) Ta có: |153| = 153; |–53| = 53.

Do đó : |153| + |–53| = 153 + 53 = 206.