tex]Буду очень благодарна, если объясните...

January 2022 2 42 Report

Сравните числа:

1) [tex]\sqrt{5}[/tex] и [tex]\frac{1}{\sqrt{5}+2 }[/tex]

2) [tex]\sqrt{7}+\sqrt{3}[/tex] и [tex]\frac{1}{\sqrt{7}-\sqrt{3} }[/tex]

Буду очень благодарна, если объясните.

taisasnitko

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Ответ:

Объяснение:1)1/(√5 +2)=(√5-2)/(√5+2)(√5-2)=(√5-2)/(5-4)=√5-2;

√5>√5 -2.

2)аналогично, 1/(√7 -√3)=(√7+√3)/(√7-√3)(√7+√3)=(√7+√3)/4,

√7 +√3>1/4(√7 +√3)

1 votes Thanks 2

TMHSH

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$1)\sqrt{5}\:\:\:\:\:\dfrac{1}{\sqrt{5} +2} \\\sqrt{5}\:\:\:\:\:\dfrac{\sqrt{5}-2}{(\sqrt{5} +2)(\sqrt{5}-2)}\\\sqrt{5}\:\:\:\:\:\dfrac{\sqrt{5} -2}{5-4} \\\sqrt{5}>\sqrt{5} -2\\\\2)\sqrt{7} +\sqrt{3} \:\:\:\:\dfrac{1}{\sqrt{7} -\sqrt{3} } \\\sqrt{7} +\sqrt{3} \:\:\:\:\dfrac{\sqrt{7} +\sqrt{3}}{(\sqrt{7} -\sqrt{3})(\sqrt{7} +\sqrt{3}) }\\\sqrt{7} +\sqrt{3}>\dfrac{\sqrt{7} +\sqrt{3}}{4 }$

1 votes Thanks 1

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