Question

Câu 1: Chứng tỏ rằng: \(8^7-2^{18}⋮14\)

Câu 2: Cho \(\dfrac{a}{2}=\dfrac{b}{5}=\dfrac{c}{7}\). Tính \(A=\dfrac{a-b+c}{a+2b-c}\)

Câu 3: Tìm GTNN của \(A=x\left(x+2\right):2\left(x-\dfrac{3}{2}\right)\)

Answer 1

Ta có:\(8^7-2^{18}=\left(2^3\right)^7-2^{18}\)\(=2^{21}-2^{18}=2^{17}\cdot2^4-2^{17}\cdot2=2^{17}\cdot\left(2^4-1\right)=2^{17}\cdot14\)\(⋮14\)

\(\Rightarrow8^7-2^{18}⋮14\)

(ĐPCM)

Answer 2

1, Ta có: \(8^7-2^{18}=2^{21}-2^{18}=2^{17}\left(2^4-2\right)=2^{17}.14⋮14\)

2, Đặt: \(\dfrac{a}{2}=\dfrac{b}{5}=\dfrac{c}{7}=k\)

\(\Rightarrow a=2k;b=5k;c=7k\)

Nên: \(A=\dfrac{a-b+c}{a+2b-c}=\dfrac{2k-5k+7k}{2k+10k-7k}=\dfrac{3k}{5k}=\dfrac{3}{5}\)

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