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\(\left(x-3\right)^2=\left(x-3\right)^3\Leftrightarrow\left(x-3\right)^3-\left(x-3\right)^2=0\)
\(\Leftrightarrow\left(x-3\right)^2\left[x-3-1\right]=0\Leftrightarrow\left(x-3\right)^2\left(x-4\right)=0\Leftrightarrow x=3;x=4\)
\(10-\left\{\left[\left(x:4+15\right):10+3.2^4\right]:10\right\}=5\)
\(\Leftrightarrow\left[\left(\dfrac{x}{4}+15\right):10+3.16\right]:10=5\)
\(\Leftrightarrow\left(\dfrac{x}{4}+15\right):10+48=50\Leftrightarrow\left(\dfrac{x}{4}+15\right):10=2\Leftrightarrow\dfrac{x}{4}+15=20\)
\(\Leftrightarrow x=20\)
a) (3⁵ . 3⁷) : 3¹⁰ + 5 . 2⁴ - 7³ : 7
= 3¹² : 3¹⁰ + 5.16 - 7²
= 3² + 80 - 49
= 9 + 31
= 40
b) (7⁵ + 7⁹) . (5⁴ + 5⁶) . (3³.3 - 9²)
= (7⁵ + 7⁹) . (5⁴ + 5⁶) . (81 - 81)
= (7⁵ + 7⁹) . (5⁴ + 5⁶) . 0
= 0
a: \(2^3-5^3:5^2+12\cdot2^2\)
\(=8-5+48\)
\(=51\)
b: \(5\cdot\left[\left(85-35:7\right):8+90\right]-5\)
\(=5\cdot\left[10+90\right]-5\)
=495
a: 2A=2^2+2^3+...+2^21
=>A=2^21-2
b: B=2+2^2+...+2^100
=>2B=2^2+2^3+...+2^101
=>B=2^101-2
c: C=3+3^2+...+3^10
=>3C=3^2+3^3+...+3^11
=>2C=3^11-3
=>C=(3^11-3)/2
`A = 2 + 2^2 + ... + 2^20`
`=> 2A = 2^2 + 2^3 + ... +2^21`
`=> 2A-A = (2^2 + 2^3 + ... + 2^21) - (2 + 2^2 + ... +2^20)`
`=> A = 2^21 - 2`
`B = 2 + 2^2 + ... + 2^99 + 2^100`
`=>2B = 2^2 + 2^3 + ... + 2^100 + 2^101`
`=> 2B-B = (2^2 + 2^3 + ... + 2^101)- (2 + 2^2 + ... + 2^100)`
`=> B = 2^101 - 2`
`C = 3 + 3^2 + .... + 3^10`
`=>3C = 3^2 + 3^3 + ... +3^11`
`=>3C - C = (3^2 + 3^3 + ... +3^11) - (3 + 3^2 + .... + 3^10)`
`=> 2C = 3^11 - 3`
`=> C = (3^11 - 3)/2
a: 39/379=195/1895<195/1890
b: \(\dfrac{193}{310}=\dfrac{6755}{10850}\)
\(\dfrac{172}{350}=\dfrac{5332}{10850}\)
mà 6755>5332
nên 193/310>172/350
24.5-310:39=100-310/39=3590/39
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