What is the answer to (sqrt(\sqrt{2)-x})(sqrt(\sqrt{x)+2})=x ?

The answer to (sqrt(\sqrt{2)-x})(sqrt(\sqrt{x)+2})=x is x\approx 1.04982…

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(sqrt(\sqrt{2)-x})(sqrt(\sqrt{x)+2})=x

Solution

(2 - x) (x + 2) = x

Solution

x \approx 1.04982 \dots

Solution steps

(2 - x) (x + 2) = x

Square both sides:

2 x + 22 - x x - 2 x = x^{2}

2 x + 22 - x x - 2 x = x^{2}

Factor

2 x + 22 - x x - 2 x : (2 + x) (2 - x)

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

Square both sides:

8 - 82 x + 4 x^{2} + 8 x - 82 x x + 4 x x^{2} + 2 x - 22 x^{2} + x^{3} = x^{4}

8 - 82 x + 4 x^{2} + 8 x - 82 x x + 4 x x^{2} + 2 x - 22 x^{2} + x^{3} = x^{4}

Move

82 x

to the right side

8 + 4 x^{2} + 8 x - 82 x x + 4 x x^{2} + 2 x - 22 x^{2} + x^{3} = x^{4} + 82 x

Move

4 x^{2}

to the right side

8 + 8 x - 82 x x + 4 x x^{2} + 2 x - 22 x^{2} + x^{3} = x^{4} + 82 x - 4 x^{2}

Move

2 x

to the right side

8 + 8 x - 82 x x + 4 x x^{2} - 22 x^{2} + x^{3} = x^{4} + 82 x - 4 x^{2} - 2 x

Move

22 x^{2}

to the right side

8 + 8 x - 82 x x + 4 x x^{2} + x^{3} = x^{4} + 82 x - 4 x^{2} - 2 x + 22 x^{2}

Move

x^{3}

to the right side

8 + 8 x - 82 x x + 4 x x^{2} = x^{4} + 82 x - 4 x^{2} - 2 x + 22 x^{2} - x^{3}

Move

8

to the right side

8 x - 82 x x + 4 x x^{2} = x^{4} + 82 x - 4 x^{2} - 2 x + 22 x^{2} - x^{3} - 8

Factor

8 x - 82 x x + 4 x x^{2} : 4 x (2 - 22 x + x^{2})

4 x (2 - 22 x + x^{2}) = x^{4} + 82 x - 4 x^{2} - 2 x + 22 x^{2} - x^{3} - 8

Square both sides:

16 x^{5} - 642 x^{4} + 192 x^{3} - 1282 x^{2} + 64 x = x^{8} - 2 x^{7} - 7 x^{6} + 42 x^{6} + 122 x^{5} + 4 x^{5} + 12 x^{4} - 322 x^{4} + 96 x^{3} - 722 x^{3} + 196 x^{2} - 642 x^{2} - 1282 x + 32 x + 64

16 x^{5} - 642 x^{4} + 192 x^{3} - 1282 x^{2} + 64 x = x^{8} - 2 x^{7} - 7 x^{6} + 42 x^{6} + 122 x^{5} + 4 x^{5} + 12 x^{4} - 322 x^{4} + 96 x^{3} - 722 x^{3} + 196 x^{2} - 642 x^{2} - 1282 x + 32 x + 64

Solve

16 x^{5} - 642 x^{4} + 192 x^{3} - 1282 x^{2} + 64 x = x^{8} - 2 x^{7} - 7 x^{6} + 42 x^{6} + 122 x^{5} + 4 x^{5} + 12 x^{4} - 322 x^{4} + 96 x^{3} - 722 x^{3} + 196 x^{2} - 642 x^{2} - 1282 x + 32 x + 64 : x \approx 0.81279 \dots, x \approx 1.04982 \dots

x \approx 0.81279 \dots, x \approx 1.04982 \dots

Verify Solutions:

x \approx 0.81279 \dots

False

, x \approx 1.04982 \dots

True

The solution is

x \approx 1.04982 \dots

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Frequently Asked Questions (FAQ)

What is the answer to (sqrt(\sqrt{2)-x})(sqrt(\sqrt{x)+2})=x ?
The answer to (sqrt(\sqrt{2)-x})(sqrt(\sqrt{x)+2})=x is x\approx 1.04982…
Solve for x: (sqrt(\sqrt{2)-x})(sqrt(\sqrt{x)+2})=x
The solution is x\approx 1.04982…

(sqrt(\sqrt{2)-x})(sqrt(\sqrt{x)+2})=x

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to (sqrt(\sqrt{2)-x})(sqrt(\sqrt{x)+2})=x ?

Solve for x: (sqrt(\sqrt{2)-x})(sqrt(\sqrt{x)+2})=x