Question
Question: If a, b, c are three distinct real numbers in G.P. If a + b + c = xb, then –...
If a, b, c are three distinct real numbers in G.P. If a + b + c = xb, then –
A
x £ – 1 or x ³ 3
B
x < – 1 or x > 3
C
x < – 3 or x > 2
D
x < – 4 or x > 3
Answer
x £ – 1 or x ³ 3
Explanation
Solution
b = ar c = ar2
a + b + c = xb
a + ar + ar2 = x a r
r2 + (1 – x) r + 1 = 0
Since r is real \ Disc. is ³ 0
(1 – x)2 – 4.1.1 ³ 0
x2 – 2x – 3 ³ 0
(x + 1) (x – 3) ³ 0
x ³ 3 or x £ – 1