What is the answer to 2sqrt(x^2-a^2)=4x-2a ?

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

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2sqrt(x^2-a^2)=4x-2a

2 x^{2} - a^{2} = 4 x - 2 a

No Solution for x \in R

Solution steps

2 x^{2} - a^{2} = 4 x - 2 a

Square both sides:

4 x^{2} - 4 a^{2} = 16 x^{2} - 16 a x + 4 a^{2}

4 x^{2} - 4 a^{2} = 16 x^{2} - 16 a x + 4 a^{2}

Solve

4 x^{2} - 4 a^{2} = 16 x^{2} - 16 a x + 4 a^{2} : x = \frac{2 a}{3} + i \frac{2 a}{3}, x = \frac{2 a}{3} - i \frac{2 a}{3}

x = \frac{2 a}{3} + i \frac{2 a}{3}, x = \frac{2 a}{3} - i \frac{2 a}{3}

Remove complex solutions:

x = \frac{2 a}{3} + i \frac{2 a}{3}, x = \frac{2 a}{3} - i \frac{2 a}{3}

No Solution for x \in R

x - 1 - 9 = 2

x, x + x - 1 = 3

2 x^{3} + 2 x^{2} + 4 x + 1 = 3

(x + 2 - x) = 2

x, - 5 + x + 6 = 3

What is the answer to 2sqrt(x^2-a^2)=4x-2a ?
The answer to 2sqrt(x^2-a^2)=4x-2a is No Solution for x\in\mathbb{R}