What is (x-8)^{1/2}-(18-x)^{1/2}>(2)^{1/2} ?

The solution to (x-8)^{1/2}-(18-x)^{1/2}>(2)^{1/2} is No Solution for x\in\mathbb{R}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(x-8)^{1/2}-(18-x)^{1/2}>(2)^{1/2}

(x - 8)^{\frac{1}{2}} - (18 - x)^{\frac{1}{2}} > (2)^{\frac{1}{2}}

No Solution for x \in R

Solution steps

(x - 8)^{\frac{1}{2}} - (18 - x)^{\frac{1}{2}} > 2^{\frac{1}{2}}

Simplify

(x - 8)^{\frac{1}{2}} - (18 - x)^{\frac{1}{2}} > 2^{\frac{1}{2}} : x - 8 - 18 - x > 2^{\frac{1}{2}}

x - 8 - 18 - x > 2^{\frac{1}{2}}

Add

18 - x

to both sides

x - 8 - 18 - x + 18 - x > 2^{\frac{1}{2}} + 18 - x

Simplify

x - 8 > 2^{\frac{1}{2}} + 18 - x

f (x) > g (x)

then

g (x) < 0 or g (x) \geq 0

For

2^{\frac{1}{2}} + 18 - x < 0 :

No Solution

For

2^{\frac{1}{2}} + 18 - x \geq 0 : x > 6 5^{\frac{1}{2}} + 15

Find singularity points

Find non-negative values for radicals:

8 \leq x \leq 18

Combine the intervals

(x > 6 5^{\frac{1}{2}} + 15 or No Solution) and 8 \leq x \leq 18

Merge Overlapping Intervals

No Solution for x \in R

x - 2 + 2 \leq x

x - 3 < x - 2

x^{2} + 1 > x - 1

x^{2} + 1 \geq 0

x < 5

What is (x-8)^{1/2}-(18-x)^{1/2}>(2)^{1/2} ?
The solution to (x-8)^{1/2}-(18-x)^{1/2}>(2)^{1/2} is No Solution for x\in\mathbb{R}