2 replies to this topic

[JayVuTF]

Giải PT sau  bằng PP Lượng Giác hóa

 

$ \sqrt{1+\sqrt{1-x^2}}(\sqrt{(1+x)^3}-\sqrt{(1-x)^3} )=2+\sqrt{1-x^2}$

 

 

[baotranthaithuy]

Giải PT sau  bằng PP Lượng Giác hóa

 

$ \sqrt{1+\sqrt{1-x^2}}(\sqrt{(1+x)^3}-\sqrt{(1-x)^3} )=2+\sqrt{1-x^2}$

ĐKXĐ: $ -1 \le x \le 1$

 

Đặt $x= cost ; t \in [0; \pi]$

 

$\Longrightarrow 2\sqrt{1+sint}(\sqrt{2}.sin^3\frac{t}{2}-\sqrt{2}.cos^3\frac{t}{2})=2+sint$

 

$\Leftrightarrow 2.(sin\frac{t}{2}+cos\frac{t}{2}).\sqrt{2}.(sin\frac{t}{2}-cos\frac{t}{2})(1+sin\frac{t}{2}.cos\frac{t}{2})=2+sint$

 

$\Leftrightarrow -\sqrt{2}.cost(2+\sint)=2+sint$

 

$\Leftrightarrow cost=\frac{-1}{\sqrt{2}} ....$

Edited by baotranthaithuy, 18-05-2015 - 21:10.

[JayVuTF]

ĐKXĐ: $ -1 \le x \le 1$

 

Đặt $x= cost ; t \in [0; \pi]$

 

$\Longrightarrow 2\sqrt{1+sint}(\sqrt{2}.sin^3\frac{t}{2}-\sqrt{2}.cos^3\frac{t}{2})=2+sint$

 

$\Leftrightarrow 2.(sin\frac{t}{2}+cos\frac{t}{2}).\sqrt{2}.(sin\frac{t}{2}-cos\frac{t}{2})(1+sin\frac{t}{2}.cos\frac{t}{2})=2+sint$

 

$\Leftrightarrow -\sqrt{2}.cost(2+ \sint )=2+sint$

 

$\Leftrightarrow cost=\frac{-1}{\sqrt{2}} ....$

Là $\Longrightarrow 2\sqrt{1+sint}(\sqrt{2}.cos^3\frac{t}{2}-\sqrt{2}.sin^3\frac{t}{2})=2+sint$

 

Đáp án $cost=\frac{1}{\sqrt{2}} ....$

Edited by JayVuTF, 20-05-2015 - 08:07.