e) 3^-1.3ⁿ+6.3^n-1=7.3⁶

<=>3^n-1+6.3^n-1=7.3⁶

<=>3^n-1.7=7.3⁶

=>3^n-1=3⁶=>n-1=6=>n=7

a+1/2=c+2/4=c+1/2=>a=c=>3a=3c

b+2/3=c+2/4=c+1/2=>b=c+1/2-2/3=c-1/6=>2b=2c-1/3

3a-2b+c=3c-2c+1/3+c=2c+1/3=105

=>2c=314/3=>c=157/3

b=c-1/6=157/3-1/6=313/6

a=c=157/3

\(< =>\sqrt{5-2x}^2=\left(3-x\right)^2\)

\(< =>5-2x=9-6x+x^2\)

\(< =>5-2x-9+6x-x^2=0\)

\(< =>-x^2+4x-4=0\)

\(< =>-\left(x-2\right)^2=0=>x-2=0=>x=2\)

3. a)x²+x=6

<=>x(x+1)=6 mà 6=2.3=2.(2+1)

=>x=2

b) 6x³+x²=2x

<=>x²(6x+1)=2x

<=>x(6x+1)=2

2=1/2.4=1/2(3+1)=1/2(6.1/2+1)

=>x=1/2

2. M=a³-a²b-ab²+b³=a²(a-b)+b²(b-a)=a²(a-b)-b²(a-b)=(a-b)(a²-b²)

=(a-b)(a-b)(a+b)=(a-b)²(a+b)

Thay a=5,75 và b=4,25 vào BT ta có

M=(5,75-4,25)²(5,75+4,25)=1,5².10 =22,5

x = 2004

=> X²⁰¹²=3²⁰¹¹.3=3^(2011+1)=3²⁰¹²

=>X=3

97

\(2+4+6+...+2n=\frac{\left(2+2n\right).n}{2}=n\left(n+1\right)=10100=100.101\Rightarrow n=100\)

<=>{x²-[6²(64-63)³-35]³-15}³=1

<=>[x²-(6².1³-35)³-15]³=1

<=>[x²-(36-35)³-15]³=1

<=>(x²-1-15)³=1

<=>(x²-16)=\(\sqrt{1}=1\)

=>x²=17=>x=\(\sqrt{17}\)