Question

Sa se afle x apartine N atfel incat : C de x luatre cate 2 + x*A de x luate cate 1 =22

Answer 1

[tex]C^2_x +xA^1_x =22 \Leftrightarrow \dfrac{x!}{2!(x-2)!} + x\cdot x =22 \Leftrightarrow \\\;\\ \Leftrightarrow \dfrac{(x-2)!\cdot (x-1)x}{2(x-2)!} +x^2 -22 =0 \Leftrightarrow \dfrac{x^2-x}{2} +x^2-22=0 \Leftrightarrow \\\;\\ \Leftrightarrow x^2-x+2x^2-44 = 0 \Leftrightarrow 3x^2-x-44 = 0 \\\;\\ \it{Solutia\  naturala\  a\  ecuatiei\  este\ x = 4}.[/tex]