90.10ⁿ -10ⁿ⁺² +10ⁿ⁺¹-20

= 90.10ⁿ  - 10ⁿ.10² + 10ⁿ .10 - 20

=10ⁿ . ( 90 - 100 + 10 ) - 20

= 10ⁿ .0 -20

= 0 - 20

= -20

=10ⁿ.(90-10²+10)-20=10ⁿ.0-20=-20

90.10ⁿ-10ⁿ⁺²+10ⁿ⁺¹-20

=90.10ⁿ-10ⁿ.10²+10ⁿ.10-20

=10ⁿ.90-10ⁿ.100+10ⁿ.10-20

=10ⁿ.(90-100+10)-20

=10ⁿ.0-20

=0-20

=-20

90.10ⁿ-10ⁿ⁺²+10ⁿ⁺¹-20

=10ⁿ⁺¹(9-10+1)-20=10ⁿ⁺¹.0-20=0-20=-20

ca nguyen thie cong thanh va le chi cuong deu dung

B3:\(\Rightarrow90.10^n-10^n.10^2+10^n.10-20\Rightarrow10^n.\left(90-10^2\right)+10^n.10-20\)

\(\Rightarrow10^n.\left(90-100\right)+10^n.10-20\Rightarrow-10.10^n+10^n.10-20\Rightarrow-20\)

\(A=-\left(x^2-x+5\right)=-\left(x^2-2.\frac{1}{2}x+\frac{1}{4}+\frac{19}{4}\right)=-\left[\left(x-\frac{1}{2}\right)^2+\frac{19}{4}\right]\)

\(=-\left(x-\frac{1}{2}\right)^2-\frac{19}{4}\le-\frac{19}{4}\)

Vậy \(A_{min}=-\frac{19}{4}\Leftrightarrow x-\frac{1}{2}=0\Rightarrow x=\frac{1}{2}\)

B2: \(\Rightarrow16x^2-8x-\left(16x^2-8x+1\right)-13\Rightarrow16x^2-8x-16x^2+8x-1-13\Rightarrow-14\)

a) Ta có:

\(90.10^k-10^{k+2}+10^{k+1}\)

\(=90.10^k-10^k.10^2+10^k.10\)

\(=10^k\left(90-10^2+10\right)\)

\(=10^k.0=0\)

b) Ta có:

\(2,5.5^{n-3}.10+5^n-6.5^{n-1}\)

\(=2,5.10.5^{n-3}+5^n-6.5^{n-1}\)

\(=5.5.5^{n-3}+5^n-6.5^{n-1}\)

\(=5^2.5^{n-3}+5^n-6.5^{n-1}\)

\(=5^{n-3+2}+5^n-6.5^{n-1}\)

\(=5^{n-1}\left(1+5-6\right)\)

\(=5^{n-1}.0=0\)

a) Rút gọn biểu thức:

\(90\times10^k-10^{k+2}+10^{k+1}=90\times10^k-10^k\times10^2+10^k\times10\) \(=10^k\times\left(90-10^2+10\right)\) \(=10^k\times\left(90-100+10\right)\) \(=10^k\times0=0\)

b) Rút gọn biểu thức:

\(2,5\times5^{n-3}\times10+5^n-6\times5^{n-1}=2,5\times\dfrac{5^n}{5^3}\times10+5^n-6\times\dfrac{5^n}{5}\) \(=2,5\times\dfrac{5^n}{125}\times10+5^n-\dfrac{6}{5}\times5^n\) \(=0,2\times5^n+5^n-1,2\times5^n\) \(=5^n\times\left(0,2+1-1,2\right)=5^n\times0=0\)

Bạn cần làm gì với biểu thức này nhỉ?

a) 10^{n + 1} - 6.10ⁿ

= 10ⁿ . 10 - 6 . 10ⁿ

= 10ⁿ . (10 - 6)

= 10ⁿ . 4

b) 2^{n + 3} + 2^{n + 2} - 2^{n + 1} + 2ⁿ

= 2ⁿ . 2³ + 2ⁿ . 2² - 2ⁿ . 2 + 2ⁿ . 1

= 2ⁿ . (8 + 4 - 2 + 1)

= 2ⁿ . 11