Câu hỏi của Nguyễn Thị Mai

Question

tính P= $\frac{2-5\sqrt{x}}{\sqrt{x}+3}$khi x =$\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}$

alibaba nguyễn · Accepted Answer

$x=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}$

$=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{\left(2\sqrt{5}-3\right)^2}}}$

$=\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}$

$=\sqrt{\sqrt{5}-\sqrt{\left(\sqrt{5}-1\right)^2}}$

$=\sqrt{1}=1$

$\Rightarrow P=\frac{2-5\sqrt{x}}{\sqrt{x}+3}=\frac{2-5}{1+3}=-\frac{3}{4}$

Câu trả lời:

$x=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}$

$=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{\left(2\sqrt{5}-3\right)^2}}}$

$=\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}$

$=\sqrt{\sqrt{5}-\sqrt{\left(\sqrt{5}-1\right)^2}}$

$=\sqrt{1}=1$

$\Rightarrow P=\frac{2-5\sqrt{x}}{\sqrt{x}+3}=\frac{2-5}{1+3}=-\frac{3}{4}$