Question

The geometric series has first term (11x-3) second term (5x-3) third term (3x-3). Find the value of x

Answer 1

Answer:

No real value of 'x'

Step-by-step explanation:

Given ,

In a Geometric progression :-

First term (a) = 11x - 3

Second term(a₂) = 5x - 3

Third term(a₃) = 3x - 3

To Find :-

Value of 'x'

How To Do :-

We know that , If a , b , c are in Geometric progression then :- b/c = c/b [ ∴ Common ratio will be same] , So by using this formula we need to equate those terms and we need to find the value of 'x'.

Formula Required :-

If a , b , c are in Geometric progression then :-

$\dfrac{b}{a}=\dfrac{c}{b}$

Cross multiplication :-

b × b = a × c

b² = ac

Solution :-

According to question :-

(11x - 3) , (5x - 3) , (3x - 3) are in geometric progression :-

→ (5x - 3)² = (11x - 3) × (3x - 3)

(5x)² + (3)² - 2(5x)(3) = 11(3x - 3) - 3(3x - 3)

25x² + 9 - 30x = 33x - 33 - 9x + 9

25x² + 9 - 30x - 33x + 33 + 9x - 9 = 0

25x² - 30x - 33x + 9x + 33 = 0

25x² - 54x + 33 = 0

Δ = b² - 4ac

= (-54)² - 4(25)(33)

= 2916 - 3300

= - 384

∴ As we got discriminant (Δ) value < 0 , So there will not be any real values of 'x'.