2 câu trả lời
`((\sqrt{15}-\sqrt{5})/(1-\sqrt{3})+(\sqrt{14}-\sqrt{7})/(1-\sqrt{2})):(1)/(\sqrt{7}-\sqrt{5})`
`=(-(\sqrt{5}(\sqrt{3}-1))/(\sqrt{3}-1)-(\sqrt{7}(\sqrt{2}-1))/(\sqrt{2}-1)):(1)/(\sqrt{7}-\sqrt{5})`
`=(-\sqrt{5}-\sqrt{7}).(\sqrt{7}-\sqrt{5})`
`=-\sqrt{35}+5-\sqrt{49}+\sqrt{35}`
`=5-7`
`=-2`
Đáp án:
$A = - 2$
Giải thích các bước giải:
Ta co :
$A = ( \frac{\sqrt[]{15}-\sqrt[]{5}}{1-\sqrt[]{3}} + \frac{\sqrt[]{14}-\sqrt[]{7}}{1-\sqrt[]{2}} ) : \frac{1}{\sqrt[]{7}-\sqrt[]{5}}$
⇔ $A = ( \frac{\sqrt[]{5}(\sqrt[]{3}-1)}{1-\sqrt[]{3}} + \frac{\sqrt[]{7}(\sqrt[]{2}-1)}{1-\sqrt[]{2}} ) . ( \sqrt[]{7} - \sqrt[]{5} )$
⇔ $A = ( - \sqrt[]{5} - \sqrt[]{7} ) . ( \sqrt[]{7} - \sqrt[]{5} )$
⇔ $A = - ( \sqrt[]{7} + \sqrt[]{5} ) . ( \sqrt[]{7} - \sqrt[]{5} )$
⇔ $A = - ( 7 - 5 )$
⇔ $A = - 2$