6^4=1296

4.9=36; 1296:36=36suy ra 4^x.9^y=36.36

ma 4.9=36 suy ra x.y=36(x chia het cho 4; y chia het cho 9) x=4;y=9

suy ra (4.9).(4.9)=1296 suy ra 4^2.9^2

thu lai

81^2;9^2.2=6561:9^4=6561;6561=1

A=2^18+2^12+2014=268 254

x=y=2

A= 2¹⁸ +2¹² + 2014 =268254

chịu@@@@@@@@@@@@@@@sorry@@@@@@@@@@@@@@@@@@

\(2^{2x}.3^{2x}=6^{\left(2x\right)}=6^4=>2x=4=>x=2.\)

\(\frac{81^x}{9^{2y}}=\frac{\left(9^2\right)^x}{9^{2y}}=9^{\left(2x-2y\right)}=9^{\left(2.2-2.y\right)}=1=9^0=>2.2-2y=0=>y=2.\)

\(A=2^{18}+2^{12}+2014=2^{12}\left(2^6+1\right)+2014.\)

1./ \(x+y=3\Rightarrow\left(x+y\right)^3=27\Rightarrow x^3+y^3+3xy\left(x+y\right)=27\Rightarrow x^3+y^3+3\cdot2\cdot3=27.\)

\(\Rightarrow x^3+y^3=9\)

2./ \(\left(x+3\right)\left(x^2-3x+3^2\right)-x^3-2x-4=0\)

\(\Leftrightarrow x^3+27-x^3-2x-4=0\Leftrightarrow2x=23\Leftrightarrow x=\frac{23}{2}\)

1/ \(x+y=3\)

\(\Rightarrow\left(x+y\right)^2=9\)

\(\Rightarrow x^2+2xy+y^2=9\)

\(\Rightarrow x^2+4+y^2=9\)

\(\Rightarrow x^2+y^2=5\)

\(\Rightarrow A=x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)=3.1=3\)

Vì \(\left(x-2\right)^4\ge0\forall x\)dấu "=" xảy ra \(\Leftrightarrow\)x-2=0 \(\Leftrightarrow\)x=2

\(\left(2y-1\right)^{2014}\ge0\forall y\)Dấu "=" xảy ra \(\Leftrightarrow\)2y - 1=0 \(\Leftrightarrow y=\frac{1}{2}\)

\(\Rightarrow\left(x-2\right)^4+\left(2y-1\right)^{2014}\ge0\)

Kết hợp với điều kiện đề bài \(\left(x-1\right)^4+\left(2y-1\right)^{2014}\le0\), ta được:

\(\left(x-2\right)^4+\left(2y-1\right)^{2014}=0\)

Vậy x = 2; \(y=\frac{1}{2}\)

Thay x=2; \(y=\frac{1}{2}\)vào M, ta có:

\(M=21.2^2.\frac{1}{2}+4.2.\left(\frac{1}{2}\right)^2\)

\(=21.4.\frac{1}{2}+4.2.\frac{1}{4}\)

\(=42+2=44\)

Vậy M=44

GIÚP MÌNH VỚI CÁC BẠN ƠI

a) \(A=2x^2+3x+1=\left(2x^2+2x\right)+\left(x+1\right)\)

\(=2x\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(2x+1\right)\)

Ta có: \(\left|x\right|=\frac{1}{2}\)\(\Leftrightarrow\orbr{\begin{cases}x=\frac{-1}{2}\\x=\frac{1}{2}\end{cases}}\)

TH1: Nếu \(x=\frac{-1}{2}\)\(\Rightarrow A=\left(\frac{-1}{2}+1\right)\left(2.\frac{-1}{2}+1\right)=\left(\frac{-1}{2}+1\right)\left(-1+1\right)=0\)

TH2: Nếu \(x=\frac{1}{2}\)\(\Rightarrow A=\left(\frac{1}{2}+1\right)\left(2.\frac{1}{2}+1\right)=\frac{3}{2}.\left(1+1\right)=\frac{3}{2}.2=3\)

Vậy \(A=0\)hoặc \(A=3\)

b) Thay \(x=-1\)và \(y=2\)vào biểu thức ta được:

\(B=\left(-1\right)^2.2-3.\left(-1\right).2^2+\left(-1\right)^2.2^2=2+12+4=18\)

2) b)

Do \(a+b+c=9\Rightarrow\left(a+b+c\right)^2=81\) 

\(\Rightarrow a^2+b^2+c^2+2\left(ab+bc+ac\right)=81\)

\(\Rightarrow2\left(ab+bc+ac\right)=81-141=-60\)

\(ab+bc+ac=-60:2=-30\)

a, B=x^3 + 3xy +y^3 = x^3 +3xy(x+y)+y^3 (vì x+y=1)

                           = (x+y)^3

                           = 1^3 =1

b, (a+b+c)^2 =a^2 +b^2 +c^2 +2ab +2bc +2ac

    9^2 = 141 +2(ab+bc+ac)

    -60 = 2(ab+bc+ac)

    ab+ac+bc=-30

Vậy M=-30

c, N =(x+y)^3 -3(x+y)(x^2+y^2) +2(x^3+y^3)

       = x^3 + 3x^2 .y + 3xy^2 + -3(x^3+xy^2 +x^2 .y+y^3)+ 2x^3 +2y^3

       = x^3 +3x^2 .y + 3xy^2 - 3x^3 -3xy^2 -3x^2 .y -3y^3 +2x^3 +2y^3

       = 0

Vậy N=0 .Chúc bạn học tốt.