Challenging quadratic questions
I'm sorry I haven't got any ideas down, but I really don't have any clue as to how to solve these. [FONT=Arial][SIZE=2]Please help me with the following questions:
1) Find all real numbers x such that x^8+x^4+x^2+2x+1 is less than or equal to 2x^6. Show all the working details.
2) If the linear graph of y=x+1 passes through the turning pointof the quadratic graph given by the rule y=x^2 + 2(m+1)x - m+1, find all the possible values of m. Show all the working details.
3) Rpove that the equation (x^2) +(y^2)-(z^2) = 1997 has infinitely many solutions in integers x, y and z. Show all the working details.