$\sqrt {a+\sqrt {b}}=\sqrt {a}+\sqrt {b}$ ise $2\sqrt {a}+\sqrt {b}=?$

Question

$\sqrt {a+\sqrt {b}}=\sqrt {a}+\sqrt {b}$

$2\sqrt {a}+\sqrt {b}=?$

Answer 1

$$\sqrt{a+\sqrt{b}}=\sqrt{a}+\sqrt{b}$$$$\Rightarrow$$$$ a+\sqrt{b}=a+b+2\sqrt{a}\cdot \sqrt{b}$$$$\Rightarrow$$$$ 2\sqrt{a}+\sqrt{b}=1$$

Answer 2

$(\sqrt{a+\sqrt{b}})^2=(\sqrt a+\sqrt b)^2\Rightarrow a+\sqrt b=a+b+2\sqrt{a.b}\Rightarrow \sqrt b=b+2\sqrt{a.b}$

$\Rightarrow \sqrt b=\sqrt b(\sqrt b+2\sqrt a)\rightarrow 1=\sqrt b+2\sqrt a$  olacaktır.