Tham khảo

\(A=\left(b+a\right)+\left(c-d\right)-\left(c+a\right)-\left(b-d\right)\)

\(A=b+a+c-d-c-a-b+d\)

\(A=\left(b-b\right)+\left(a-a\right)+\left(c-c\right)+\left(-d+d\right)\)

\(A=0\)

\(B=\left(a-d\right)-\left(d+a\right)-\left(c-d\right)+\left(c+b\right)\)

\(B=a-d-d-a-c+d+c+b\)

\(B=\left(a-a\right)+\left(d-d+d\right)+\left(-c+c\right)+b\)

\(B=d+b\)

a) Ta có: \(A=\left(b+a\right)+\left(c-d\right)-\left(c+a\right)-\left(b-d\right)\)

\(=a+b+c-d-c-a-b+d\)

=0

b) Ta có: \(B=\left(a-d\right)-\left(a+d\right)-\left(c-d\right)+\left(c+b\right)\)

\(=a-d-a-d-c+d+c+b\)

=b-d

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

`A=sqrt{x-2}+sqrt{6-x}(2<=x<=6)`
Áp dụng BĐT `sqrtA+sqrtB>=sqrt{A+B}`
`=>A>=sqrt{x-2+6-x}=2`
Dấu "=" `<=>x=2` hoặc `x=6`
Áp dụng BĐT bunhia
`=>A<=sqrt{2(x-2+6-x)}=2sqrt2`
Dấu "=" `<=>x=4`
`C=sqrt{1+x}+sqrt{8-x}(-1<=x<=8)`
Áp dụng BĐT `sqrtA+sqrtB>=sqrt{A+B}`
`=>A>=sqrt{1+x+8-x}=3`
Dấu "=" `<=>x=-1` hoặc `x=8`
Áp dụng BĐT bunhia
`=>A<=sqrt{2(1+x+8-x)}=3sqrt2`
Dấu "=" `<=>x=7/2`

`D=2sqrt{x+5}+sqrt{1-2x}(-5<=x<=1/2)`
`=sqrt{4x+20}+sqrt{1-2x}`
Áp dụng BĐT `sqrtA+sqrtB>=sqrt{A+B}`
`=>D>=sqrt{4x+20+1-2x}=sqrt{2x+21}`
Mà `x>=-5`
`=>D>=sqrt{-10+21}=sqrt{11}`
Dấu "=" `<=>x=-5`

A= (-2a + 3b -4c) - (-2a - 3b -4c)

A= -2a + 3b -4c + 2a + 3b + 4c

A=6b(Mà b=-1)

         Suy ra:A=6.(-1)=-6

Vậy A=-6

a/b=b/c=c/d=d/a=(a+b+c+d)/(b+c+d+a)=1

>a=b=c=d>tự tính