Câu 75 Trang 40: Chứng minh đẳng thức
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Câu 75 Trang 40: Chứng minh đẳng thức

Ta có :

a.  

Xét   $VT=\left ( \frac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\frac{\sqrt{216}}{3} \right ).\frac{1}{\sqrt{6}}$

$VT=\left ( \frac{\sqrt{6} (\sqrt{2}-1)}{2(\sqrt{2}-1)}\right ).\frac{1}{\sqrt{6}}$

$VT=\left ( \frac{\sqrt{6}}{2}-2\sqrt{6} \right ).\frac{1}{\sqrt{6}}$

$VT=\left ( \frac{-3}{2}.\sqrt{6} \right ).\frac{1}{\sqrt{6}}$

$VT=-\frac{3}{2}=-1,5$

Nhận xét : VT = VP = - 1,5

=>   ( đpcm ).

b.  

Xét   $VT=\left ( \frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}} \right ):\frac{1}{\sqrt{7}-\sqrt{5}}$

$VT=\left ( \frac{\sqrt{7}(\sqrt{2}-1)}{1-\sqrt{2}}+\frac{\sqrt{5(\sqrt{3}-1)}}{1-\sqrt{3}} \right ):\frac{1}{\sqrt{7}-\sqrt{5}}$

$VT=(-\sqrt{7}-\sqrt{5})(\sqrt{7}-\sqrt{5})$

$VT=-(\sqrt{7}+\sqrt{5})(\sqrt{7}-\sqrt{5})=-(7-5)=-2$

Nhận xét : VT = VP = - 2 

=>  ( đpcm ).

c.   

Xét   $VT=\frac{a\sqrt{b}+b\sqrt{a}}{\sqrt{ab}}:\frac{1}{\sqrt{a}-\sqrt{b}}$

$VT=\frac{\sqrt{ab}(\sqrt{a}+\sqrt{b})}{\sqrt{ab}}:\frac{1}{\sqrt{a}-\sqrt{b}}$

$VT=\frac{\sqrt{ab}(\sqrt{a}+\sqrt{b})}{\sqrt{ab}}.{\sqrt{a}-\sqrt{b}}=a-b$

Nhận xét : VT = VP = a - b 

=>  ( đpcm ).

d.

Xét   $VT=\left ( 1+\frac{a+\sqrt{a}}{\sqrt{a}+1} \right )\left ( 1-\frac{a-\sqrt{a}}{\sqrt{a}-1} \right )$

$VT=\left ( 1+\frac{\sqrt{a}(\sqrt{a}+1)}{\sqrt{a}+1} \right )\left ( 1-\frac{\sqrt{a}(\sqrt{a}-1)}{\sqrt{a}-1} \right )$

$VT=(1+\sqrt{a})(1-\sqrt{a})=1-a$

Nhận xét : VT = VP = 1 - a 

=>  ( đpcm ).

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Hi, I'm David Smith

I'm David Smith, husband and father , I love Photography,travel and nature. I'm working as a writer and blogger with experience of 5 years until now.

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