Question

S is a geometric sequence. (Square root x-1),1 and (square root x+1) are the first three terms of s. Find the value of x.

Answer 1

Answer:

2

Step-by-step explanation:

(√x - 1) / 1 = 1 / (√x + 1)

√x - 1 = 1 / (√x + 1)

√x - 1 =  √x - 1 / (√x + 1)(√x - 1)

√x - 1 =  √x - 1 / x - 1

(√x - 1)(x - 1) = √x - 1

x - 1 = 1

x = 2

Answer 2

Answer:

x = ± $\sqrt{2}$

Step-by-step explanation:

given the 3 terms of a geometric sequence

$\sqrt{x-1}$, 1, $\sqrt{x+1}$, then the common ratio r

r = $\frac{\sqrt{(x+1)} }{1}$ = $\frac{1}{\sqrt{(x-1)} }$ ( cross- multiply )

$\sqrt{(x+1)(x-1)}$ = 1 ( square both sides )

(x + 1 )(x - 1 ) = 1 ← expand factors on left side )

x² - 1 = 1 ( add 1 to both sides )

x² = 2 ( take the square root of both sides )

x = ± $\sqrt{2}$