Đáp án:
$1)A=72\\ 2)x^2+y^2=53\\ x^2-y^2=\pm 45\\ x^3-y^3=\pm 335\\ x^4+y^4=2417\\ x^5+y^5=16839$
Giải thích các bước giải:
$1)x^3-x=8\\ A=x^6-2x^4-x+x^2+x^3\\ =x^6-x^4-x^4+x^2+x^3-x\\ =x^3(x^3-x)-x(x^3-x)+x^3-x\\ =(x^3-x)(x^3-x+1)\ =8(8+1)\\ =72\\ 2) x+y=9 ; xy=14\\ \circledast x^2+y^2\\ =x^2+2xy+y^2-2xy\\ =(x+y)^2-2xy\\ =9^2-2.14\\ =53\\ \circledast x^2-y^2\\ (x-y)^2=x^2-2xy+y^2=53-2.14=25\\ \Rightarrow x-y=\pm 5\\ x^2-y^2=(x-y)(x+y)\\ =9(x-y)\\ =\pm 9.5\\ =\pm 45\\ \circledast x^3-y^3\\ =(x-y)(x^2+xy+y^2)\\ =\pm 5(53+14)\\ =\pm 335\\ \circledast x^4+y^4\\ =x^4+2x^2y^2+y^4-2x^2y^2\\ =(x^2+y^2)^2-2(xy)^2\\ =53^2-2.14^2\\ =2417\\ \circledast x^5+y^5\\ =x^5+x^4y-x^4y-x^3y^2+x^3y^2+x^2y^3-x^2y^3-xy^4+xy^4+y^5\\ =x^4(x+y)-x^3y(x+y)+x^2y^2(x+y)-xy^3(x+y)+y^4(x+y)\\ =(x+y)(x^4-x^3y+x^2y^2-xy^3+y^4)\\ =(x+y)(x^4+y^4-x^3y-xy^3+x^2y^2)\\ =(x+y)(x^4+y^4-xy(x^2+y^2)+x^2y^2)\\ =9(2417-14.53+14^2)\\ =16839$
