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3 years ago

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.

Mathematics

2 answers:

rosijanka [135]3 years ago

8 0

Answer:

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

lora16 [44]3 years ago

4 0

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 = ± $\sqrt{2}$

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4) reflexive property of congruence

5) SAS theorem

6) property of Congruent triangles

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3 years ago

Directions: Find the complemen

andre [41]

Given:

The angles are:

Example $54^\circ$

1. $63^\circ$

2. $87^\circ$

3. $45^\circ$

4. $72^\circ$

5. $5^\circ$

To find:

The complimentary angle of the given angles.

Solution:

If two angles are complimentary, then their sum is 90 degrees.

Example: Let x be the complimentary angle of $54^\circ$ , then

$x+54^\circ=90^\circ$

$x=90^\circ -54^\circ$

$x=36^\circ$

Similarly,

1. The complimentary angle of $63^\circ$ is:

$90^\circ -63^\circ=27^\circ$

2. The complimentary angle of $87^\circ$ is:

$90^\circ -87^\circ=3^\circ$

3. The complimentary angle of $45^\circ$ is:

$90^\circ -45^\circ=45^\circ$

4. The complimentary angle of $72^\circ$ is:

$90^\circ -72^\circ=18^\circ$

5. The complimentary angle of $5^\circ$ is:

$90^\circ -5^\circ=85^\circ$

Therefore, the complimentary angles of $54^\circ, 63^\circ, 87^\circ, 45^\circ, 72^\circ, 5^\circ$ are $36^\circ, 27^\circ, 3^\circ, 45^\circ, 18^\circ, 85^\circ$ respectively.

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