Question

Tìm x để:

a) (2x⁴-3x³+4x+1)\(⋮\)(x²-1)

b) (x⁵+2x⁴+3x²+x-3)\(⋮\)(x²+1)

m.n jup mk vs ạk

Answer 1

a: \(2x^4-3x^3+4x+1⋮x^2-1\)

\(\Leftrightarrow2x^4-2x^2-3x^3+3x+2x^2-2+x+3⋮x^2-1\)

\(\Leftrightarrow x+3⋮x^2-1\)

\(\Leftrightarrow x^2-9⋮x^2-1\)

\(\Leftrightarrow x^2-1\in\left\{1;-1;2;-2;4;-4;8;-8\right\}\)

\(\Leftrightarrow x\in\left\{\sqrt{2};-\sqrt{2};0;\sqrt{3};-\sqrt{3};\sqrt{5};-\sqrt{5};3;-3\right\}\)

b: \(x^5+2x^4+3x^2+x-3⋮x^2+1\)

\(\Leftrightarrow x^5+x^3+2x^4+2x^2-x^3-x+x^2+1+2x-4⋮x^2+1\)

\(\Leftrightarrow2x-4⋮x^2+1\)

\(\Leftrightarrow4x^2-16⋮x^2+1\)

\(\Leftrightarrow4x^2+4-20⋮x^2+1\)

\(\Leftrightarrow x^2+1\in\left\{1;2;4;5;10;20\right\}\)

hay \(x\in\left\{0;1;-1;\sqrt{3};-\sqrt{3};2;-2;3;-3;\sqrt{19};-\sqrt{19}\right\}\)