- #1
Karol
- 1,380
- 22
Homework Statement
Homework Equations
$$a^2-b^2=(a-b)(a+b)$$
The Attempt at a Solution
$$a^2=\sqrt{1-x_2^2}\,\,\, ,\ \ b^2=\sqrt{1-x_1^2}$$
$$|a^2-b^2|=\left| \sqrt{1-x_2^2}-\sqrt{1-x_1^2} \right|=\left| \sqrt[4]{1-x_2^2} - \sqrt[4]{1-x_1^2} \right|\cdot\left| \sqrt[4]{1-x_2^2} + \sqrt[4]{1-x_1^2} \right|$$
I have to reach:
$$\left| \sqrt{y_2} - \sqrt{y_1} \right| \leq \sqrt{\sqrt{1-x_2^2} - \sqrt{1-x_1^2} }$$