Let a and b be the roots of 7x^2 - x - 3 = 0. Find (1 + a + a^2 + a^3 +.....) (1 + b + b^2 + b^3 +.....).
Thx :)
+23252 Hint:
1) Use the quadratic formula to find the two solutions to the equation: 7x2 - x - 3 = 0.
Leave them in reduced radical form.
Label one solution as 'a' and the other as 'b'.
Note that each solution is in the range: -1 < x < 1,
2) 1 + a + a2 + a3 + ... is an infinite geometric series, whose sum can be found
using the formula: Sum = (first term) / [ 1 - (common ratio) ]
the first term is 1, and the common ratio is the solution that you found in step 1.
This formula applies because the common ration is in the range -1 < r < 1.
3) You can find the sum of 1 + + b2 + b3 + ... in a similar way and multiply these
two answers.
