Question

If a b c are three distinct real numbers in gp and a+b+c=xb then x cannot be

Answer 1

Question:

If a b c are three distinct real numbers in G.P and a + b + c = xb then x cannot be -2, -3, 4, 2 ?

Answer:

2.

Step-by-step explanation:

Since, a, b and are in G.P.

› b² = ac

Since, a + b + c = xb.

› (a + c) = (x - 1)b

Take square on both sides,

› a² + c² + 2ac = (x - 1)²b² [b² = ac]

› a² + c² = (x - 1)²ac - 2ac

› a² + c² = ac[(x - 1)² - 2]

› a² + c² = ac[x² - 2x - 1]

Since, a² + c² and b² = ac are positive.

Then, x² - 2x - 1 would be positive but for x = 2, x² - 2x - 1 is negative

Hence, we cannot take x as 2.