What is the answer to sqrt(x-1)+2x+sqrt(1-x)=4 ?

The answer to sqrt(x-1)+2x+sqrt(1-x)=4 is No Solution for x\in\mathbb{R}

Solve for x: sqrt(x-1)+2x+sqrt(1-x)=4

The solution is No Solution for x\in\mathbb{R}

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sqrt(x-1)+2x+sqrt(1-x)=4

Solution

x - 1 + 2 x + 1 - x = 4

Solution

No Solution for x \in R

Solution steps

x - 1 + 2 x + 1 - x = 4

Remove square roots

1 - x = \frac{4 x ^{4} - 36 x ^{3} + 117 x ^{2} - 162 x + 81}{16 - 16 x + 4 x ^{2}}

Switch sides

4 x^{2} + 4 1 - x x - 17 x + 17 - 8 1 - x = x - 1

Move

4 x^{2}

to the right side

4 1 - x x - 17 x + 17 - 8 1 - x = x - 1 - 4 x^{2}

Move

17 x

to the right side

4 1 - x x + 17 - 8 1 - x = - 4 x^{2} + 18 x - 1

Move

17

to the right side

4 1 - x x - 8 1 - x = - 4 x^{2} + 18 x - 18

Subtract

- 4 x^{2} + 18 x - 18

from both sides

4 1 - x x - 8 1 - x - (- 4 x^{2} + 18 x - 18) = - 4 x^{2} + 18 x - 18 - (- 4 x^{2} + 18 x - 18)

Simplify

4 x 1 - x - 8 1 - x + 4 x^{2} - 18 x + 18 = 0

Factor

4 x 1 - x - 8 1 - x + 4 x^{2} - 18 x + 18 : 2 (2 x 1 - x - 4 1 - x + 2 x^{2} - 9 x + 9)

2 (2 x 1 - x - 4 1 - x + 2 x^{2} - 9 x + 9) = 0

Divide both sides by

2

2 x 1 - x - 4 1 - x + 2 x^{2} - 9 x + 9 = 0

Move

2 x^{2}

to the right side

2 x 1 - x - 4 1 - x - 9 x + 9 = - 2 x^{2}

Move

9 x

to the right side

2 x 1 - x - 4 1 - x + 9 = - 2 x^{2} + 9 x

Move

9

to the right side

2 x 1 - x - 4 1 - x = - 2 x^{2} + 9 x - 9

Factor

2 x 1 - x - 4 1 - x : 2 1 - x (x - 2)

2 1 - x (x - 2) = - 2 x^{2} + 9 x - 9

Divide both sides by

2 (x - 2)

1 - x = \frac{- 2 x ^{2} + 9 x - 9}{2 ( - 2 + x )}

Solve

1 - x = \frac{4 x ^{4} - 36 x ^{3} + 117 x ^{2} - 162 x + 81}{16 - 16 x + 4 x ^{2}} :

No Solution for

x \in R

No Solution for x \in R

Popular Examples

x-3=sqrt(10x+9)

x - 3 = 10 x + 9

(x-2)^{2/3}=100

(x - 2)^{\frac{2}{3}} = 100

sqrt(b)+5=11

b + 5 = 11

sqrt(x+7)=9

x + 7 = 9

w^2-2sqrt(2w)=-2

w^{2} - 2 2 w = - 2

Frequently Asked Questions (FAQ)

What is the answer to sqrt(x-1)+2x+sqrt(1-x)=4 ?
The answer to sqrt(x-1)+2x+sqrt(1-x)=4 is No Solution for x\in\mathbb{R}
Solve for x: sqrt(x-1)+2x+sqrt(1-x)=4
The solution is No Solution for x\in\mathbb{R}