Theory question 102
Progressions(a) Simplify: (x2 − 8x + 16)/(x2 − 7x + 12)
(b) If 1/2, 1/x, 1/3 are successive terms of an arithmetic progression (A.P.), show that (2 − x)/(x − 3) = 2/3.
Show the model answer
Model answer
(a) (x − 4)(x − 4)/[(x − 4)(x − 3)] = (x − 4)/(x − 3).
(b) Equal common difference: 1/x − 1/2 = 1/3 − 1/x.
So (2 − x)/2x = (x − 3)/3x. Multiply by 6x: 3(2 − x) = 2(x − 3).
Hence (2 − x)/(x − 3) = 2/3.
Explanation
In an AP the difference between consecutive terms is constant.