What is the answer to 1-x=sqrt(1-x\sqrt{4-7x^2)} ?

The answer to 1-x=sqrt(1-x\sqrt{4-7x^2)} is x=0,x= 1/2

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1-x=sqrt(1-x\sqrt{4-7x^2)}

1 - x = 1 - x 4 - 7 x^{2}

x = 0, x = \frac{1}{2}

Solution steps

1 - x = 1 - x 4 - 7 x^{2}

Square both sides:

1 - 2 x + x^{2} = 1 - x 4 - 7 x^{2}

1 - 2 x + x^{2} = 1 - x 4 - 7 x^{2}

Subtract

1 - x 4 - 7 x^{2}

from both sides

1 - 2 x + x^{2} - (1 - x 4 - 7 x^{2}) = 1 - x 4 - 7 x^{2} - (1 - x 4 - 7 x^{2})

Simplify

x^{2} + 4 - 7 x^{2} x - 2 x = 0

Factor

x^{2} + 4 - 7 x^{2} x - 2 x : x (x + 4 - 7 x^{2} - 2)

x (x + 4 - 7 x^{2} - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x + 4 - 7 x^{2} - 2 = 0

Solve

x + 4 - 7 x^{2} - 2 = 0 : x = \frac{1}{2}, x = 0

x = 0, x = \frac{1}{2}

Verify Solutions:

x = 0

True

, x = \frac{1}{2}

True

The solutions are

x = 0, x = \frac{1}{2}

5 x + 5 = 5

2 x^{\frac{4}{3}} = 162

x + 7 = 5

x - 3 = x - 1

x = 2 x 1 - x^{2}

What is the answer to 1-x=sqrt(1-x\sqrt{4-7x^2)} ?
The answer to 1-x=sqrt(1-x\sqrt{4-7x^2)} is x=0,x= 1/2
Solve for x: 1-x=sqrt(1-x\sqrt{4-7x^2)}
The solution is x=0,x= 1/2