If a and b satisfy the equations `...a+1/b=4 and 1/a+b=16/15.` determine products of all possible values of ab.

Let a in (0,1] satisfies the equation a^(2008)-2a+1=0 and S=1+a+a^2+.....+a^2007 Then sum of all possible values of S is a. 2010 b. 2009 c. 2008 d. 2

Let a in (0,1] satisfies the equation a^(2008)-2a+1=0 and S=1+a+a^2+.....+a^2007 Then sum of all possible values of S is a. 2010 b. 2009 c. 2008 d. 2

Let a in(0,1] satisfies the equation a^(2008)-2a+1=0 and S=1+a+a^(2)+....+a^(2007) Then sum of all possible values of S is a.2010 b.2009 c.2008 d.2

Integers a, b, c satisfy a + b - c = 1 and a^2 + b^2 - c^2 = -1 . What is the sum of all possible values of a^(2) + b^(2) + c^(2) ?

If |-3a+15|=6 and |-2b+12|=4 , what is the greatest possible value of ab ?

Integers a,b,c satisfy a+b-c=1 and a^(2)+b^(2)-c^(2)=-1 What is the sum of all possible values of a^(2)+b^(2)+c^(2)?

If a,b in I and satisfy the equation a(b-1)=3+b-b^(2), then find the greatest value of |a+b|

If a and b are the roots of the equation x^(2) - kx + 16 = 0 and satisfy a^(2) + b^(2) = 32, then the value of k is