Câu hỏi của BÍCH THẢO

Question

Toán nâng cao !!

Toru · Accepted Answer

$A=\dfrac{x+15}{x-2}=\dfrac{x-2+17}{x-2}$ $\left(ĐK:x\ne2\right)$

$=\dfrac{x-2}{x-2}+\dfrac{17}{x-2}=1+\dfrac{17}{x-2}$

Để $A=1+\dfrac{17}{x-2}\in Z$

thì $\dfrac{17}{x-2}\in Z$

$\Rightarrow17⋮x-2$

$\Rightarrow x-2\inƯ\left(17\right)$

$\Rightarrow x-2\in\left\{1;17;-1;-17\right\}$

$\Rightarrow x\in\left\{3;19;1;-15\right\}\left(tm\right)$

$Vậy:x\in\left\{3;19;1;-15\right\}$

Câu trả lời:

$A=\dfrac{x+15}{x-2}=\dfrac{x-2+17}{x-2}$ $\left(ĐK:x\ne2\right)$

$=\dfrac{x-2}{x-2}+\dfrac{17}{x-2}=1+\dfrac{17}{x-2}$

Để $A=1+\dfrac{17}{x-2}\in Z$

thì $\dfrac{17}{x-2}\in Z$

$\Rightarrow17⋮x-2$

$\Rightarrow x-2\inƯ\left(17\right)$

$\Rightarrow x-2\in\left\{1;17;-1;-17\right\}$

$\Rightarrow x\in\left\{3;19;1;-15\right\}\left(tm\right)$

$Vậy:x\in\left\{3;19;1;-15\right\}$

Kiều Vũ Linh · Answer

Ta có:

x + 15 = x - 2 + 17

Để A ∈ Z thì (x + 15) ⋮ (x - 2)

⇒ 17 ⋮ (x - 2)

⇒ x - 2 ∈ Ư(17) = {-17; -1; 1; 17}

⇒ x ∈ {-15; 1; 3; 19}

Câu trả lời:

Ta có:

x + 15 = x - 2 + 17

Để A ∈ Z thì (x + 15) ⋮ (x - 2)

⇒ 17 ⋮ (x - 2)

⇒ x - 2 ∈ Ư(17) = {-17; -1; 1; 17}

⇒ x ∈ {-15; 1; 3; 19}

BÍCH THẢO · Answer

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Câu trả lời:

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