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shulgina200025
@shulgina200025
November 2021
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lsryvkina
Пусть А=√(27+10√2) -√(27-10√2)
Найдем А^2 по формуле: (а-в)^2=a^2-2ab+b^2
А^2=(√(27+10√2))^2 -2√(27+10√2)√(27-10√2) +(√(27-10√2))^2=
= 27+10√2 - 2√(27^2-(10√2)^2) +27-10√2=54-2√(729-200)=54-2√529=
= 54-2*23=54-46=8
Итак, А^2=8, значит, А=√8=√(4*2)=2√2
Ответ:2√2
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Answers & Comments
Найдем А^2 по формуле: (а-в)^2=a^2-2ab+b^2
А^2=(√(27+10√2))^2 -2√(27+10√2)√(27-10√2) +(√(27-10√2))^2=
= 27+10√2 - 2√(27^2-(10√2)^2) +27-10√2=54-2√(729-200)=54-2√529=
= 54-2*23=54-46=8
Итак, А^2=8, значит, А=√8=√(4*2)=2√2
Ответ:2√2