Question

Tìm SN x, sao cho: x mũ 2-9x+7 chia hết cho x-9

Answer 1

Ta có: \(x^2-9x+7⋮x-9\)

mà \(x^2-9x⋮x-9\)

nên \(7⋮x-9\)

\(\Leftrightarrow x-9\inƯ\left(7\right)\)

\(\Leftrightarrow x-9\in\left\{1;-1;7;-7\right\}\)

hay \(x\in\left\{10;8;16;2\right\}\)

Vậy: \(x\in\left\{10;8;16;2\right\}\)

Answer 2

\(x^2\) -9x+7⋮x-9

x(x-9)+7⋮x-9

Vì x-9⋮x-9

nên x(x-9)+7⋮x-9

⇒x-9∈ Ư(7)

Ư(7)={1;-1;7;-7}

x-9	1	-1	7	-7
x	10	-8	16	2

⇒x∈{10;-8;16;-2}