2,5x5^n x 10+5^n-6x5^n-1
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a) \(5^{3n+2}=25^{n+3}\)
\(\Leftrightarrow5^{3n+2}=5^{2\left(n+3\right)}\)
\(\Leftrightarrow3n+2=2\left(n+3\right)\)
\(\Leftrightarrow3n+2=2n+6\)
\(\Leftrightarrow n=4\)
b) \(6.5^{n-2}+10^2=2.5^3\left(n>1\right)\)
\(\Leftrightarrow6.5^{n-2}=2.5^3-10^2\)
\(\Leftrightarrow6.5^{n-2}=2.5^3-2^2.5^2\)
\(\Leftrightarrow6.5^{n-2}=2.5^2\left(5-2\right)\)
\(\Leftrightarrow6.5^{n-2}=2.5^2.3\)
\(\Leftrightarrow5^{n-2}=5^2\)
\(\Leftrightarrow n-2=2\)
\(\Leftrightarrow n=4\)
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![](https://rs.olm.vn/images/avt/0.png?1311)
\(\cdot\) `\text {dnammv}`
`7,`
`a,`
`M(x)=\(-5x^4+3x^5+x\left(x^2+5\right)+14x^4-6x^5-x^3+x-1\)
`M(x)=-5x^4+3x^5+x^3+5x+14x^4-6x^5-x^3+x-1`
`=(3x^5-6x^5)+(-5x^4+14x^4)+(x^3-x^3)+(5x+x)-1`
`=-3x^5+9x^4+6x-1`
`N(x)=x^4(x - 5) - 3x^3 + 3x + 2x^5 - 4x^4 + 3x^3 - 5`
`= x^5-5x^4-3x^3+3x+2x^5-4x^4+3x^3-5`
`= 3x^5-9x^4+3x-5`
`b,`
`H(x)= N(x)+ M(x)`
`-> H(x)=(-3x^5+9x^4+6x-1)+(3x^5-9x^4+3x-5)`
`= -3x^5+9x^4+6x-1+3x^5-9x^4+3x-5`
`= (-3x^5+3x^5)+(9x^4-9x^4)+(6x+3x)+(-1-5)`
`= 9x-6`
`G(x)=M(x)-N(x)`
`-> G(x)= (-3x^5+9x^4+6x-1)-(3x^5-9x^4+3x-5)`
`= -3x^5+9x^4+6x-1-3x^5+9x^4-3x+5`
`= (-3x^5-3x^5)+(9x^4+9x^4)+(6x-3x)+(-1+5)`
`= -6x^5+18x^4+3x+4`
`c,`
`H(x)=9x-6`
Hệ số cao nhất: `9`
Hệ số tự do: `-6`
`G(x)= -6x^5+18x^4+3x+4`
Hệ số cao nhất: `-6`
Hệ số tự do: `4`
`d,`
`H(1)=9*1-6=9-6=3`
`H(-1)=9*(-1)-6=-9-6=-15`
`G(1)=-6*1^5+18*1^4+3*1+4=-6+18+3+4=12+3+4=15+4=19`
`G(0)=-6*0^5+18*0^4+3*0+4=0+0+0+4=4`
`H(x)=9x-6=0`
`-> 9x=0+6`
`-> 9x=6`
`-> x= 6 \div 9`
`-> x=`\(\dfrac{2}{3}\)
Vậy, nghiệm của đa thức là `x=`\(\dfrac{2}{3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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=(30+7-37)x(1+2+3+4+5+6+7+8+9+10)
=(37-37)x(1+2+3+4+5+6+7+8+9+10)
=0x(1+2+3+4+5+6+7+8+9+10)
=0
![](https://rs.olm.vn/images/avt/0.png?1311)
=(30+7-37)*(1+2+3+4+5+6+7+8+9+10)
=0*(1+2+3+4+5+6+7+8+9+10)
=0
( 6 x 5 + 7 - 37)x (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 +9 + 10)
0 x 55 = 0
rút gọn biểu thức nha cb