ta có: x² + x = 0

=> x(x + 1) = 0

=> \(\hept{\begin{cases}x=0\\x+1=0\end{cases}}\)

=> \(\hept{\begin{cases}x=0\\x=-1\end{cases}}\)

chúc bạn học giỏi!! ^^

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x²+x=0

=>x=0 hoặc x=-1

Ví dụ:

0²+0=0

-(1)²+-1=0

1,

Có \(\sqrt{x}\ge0\)với mọi x

=> 2 + \(\sqrt{x}\ge\)2 với mọi x

=> A \(\ge\)2 với mọi x

Dấu "=" xảy ra <=> \(\sqrt{x}=0\)<=> x = 0

KL: A_min = 2 <=> x = 0

2, (câu này phải là GTLN chứ nhỉ)

Có \(\sqrt{x-1}\ge0\)với mọi x

=> \(2.\sqrt{x-1}\ge0\)với mọi x

=> \(5-2.\sqrt{x-1}\le5\)với mọi x

=> B \(\le\)5 với mọi x

Dấu "=" xảy ra <=> \(\sqrt{x-1}=0\)<=> x - 1 = 0 <=> x = 1

KL B_max = 5 <=> x = 1

\(\sqrt{x}\ge0\)

\(\Rightarrow A=2+\sqrt{x}\ge2+0\ge2\)

\(MinA=2\Leftrightarrow\sqrt{x}=0\Rightarrow x=0\)

2) \(5-2\sqrt{x-1}\le5\)

\(MinA=5\Leftrightarrow x-1=0\Rightarrow x=1\)

\(\left|5\left(2x+3\right)\right|+\left|2\left(2x+3\right)\right|+\left|2x+3\right|=16\)

\(=8\left(2x+3\right)=16\)

\(\Rightarrow2x+3=2\)

\(\Rightarrow x=-\frac{1}{2}\)

-{-[-(3/4)]}=3/4

83/41

83/41

\(\text{Ta có: }\)\(\frac{1}{90}-\frac{1}{72}-\frac{1}{56}-\frac{1}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)

\(=\frac{1}{90}-\left(\frac{1}{72}+\frac{1}{56}+\frac{1}{42}+\frac{1}{30}+\frac{1}{20}+\frac{1}{12}+\frac{1}{6}+\frac{1}{2}\right)\)

\(=\frac{1}{90}-\left(\frac{1}{9.8}+\frac{1}{8.7}+\frac{1}{7.6}+\frac{1}{6.5}+\frac{1}{5.4}+\frac{1}{4.3}+\frac{1}{3.2}+\frac{1}{2.1}\right)\)

\(=\frac{1}{90}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{8}-\frac{1}{9}\right)\)

\(=\frac{1}{90}-\left(1-\frac{1}{9}\right)\)

\(=\frac{1}{90}-\frac{8}{9}=-\frac{81}{90}=-\frac{9}{10}\)

<=> 

D = 1/90+1/72+1/56+1/42+1/30+1/20+1/12+1/6+1/2

D = 1/(1x2) + 1/(2x3) + 1/(3x4) + 1/(4x5) + 1/(5x6) + … + 1/(9x10)

D = 1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + …. + 1/9 – 1/10

D = 1 – 1/10

D = 9/10

A=1+3/2^3+4/2^4+5/2^5+...100/2^100 
1/2*A = 1/2 + 3/2^4 + 4/2^5 +....+ 99/2^100 + 100/2^101 

A- A/2 = 1/2A =1/2 + 3/2^3 + 1/2^4 +...+1/2^100 - 100/2^101= 

Tham khảo bài này nha
= [1/2+1/2^2 +1/2^3 +...+1/2^100] -100/2^101 (Do 3/2^3 = 1/2^2 +1/2^3) 

=[1-(1/2)^101]/(1-1/2) -100/2^101 = 

=(2^101 -1)/2^100 - 100/2^101 

=> A= (2^101 -1)/2^99 - 100/2^100 

25 + 62 + 31 + 8 + 2

= ( 62 + 8 ) + ( 25 + 31 + 2 )

=     70      +     58

=         128                    k nha

25 + 62 + 31 + 8 + 2

= 87 + 31 + 10

= 118 + 10

= 128

Ta có:

A = 7ⁿ⁺² - 7ⁿ - 5ⁿ⁺² + 5ⁿ

A = 7ⁿ.(7² - 1) - 5ⁿ.(5² - 1)

A = 7ⁿ.(49 - 1) - 5ⁿ.(25 - 1)

A = 7ⁿ.48 - 5ⁿ.24

A = 24.(7ⁿ.2 - 5ⁿ) chia hết cho 24 (đpcm)

A = 7^{n + 2} - 7ⁿ - 5^{n + 2} + 5ⁿ = 7ⁿ . 49 - 7ⁿ - 5ⁿ . 25 + 5ⁿ

=> A = 7ⁿ . (49 - 1) + 5ⁿ . (-25 + 1)

=> A = 7ⁿ . 48 + 5ⁿ . (-24)

Do: 7ⁿ . 48 = 7ⁿ . 2 . 24 chia hết cho 24 và 5ⁿ . (-24) chia hết cho 24

=> A = 7ⁿ . 48 + 5ⁿ . (-24) chia hết cho 24

Vậy A chia hết cho 24