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NITROLEX
@NITROLEX
July 2022
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Помогите пожалуйста подробно решить. Ответ - (-5).
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oganesbagoyan
Verified answer
( √(12+6√3) -
√(11-6√2) ) /(√2 -√3)
+ √24 =
( (
3+√3) -(3-√2)
) /
(√2 -√3) + √24 = - (√3 +√2)
/(
√3 -√2) +2√6 =
= - (√3 +√2)(√3 +√2(
/
(√3 -√2)(√3 +√2) +2√6 = -(√3+√2)² /
(
(√3)² -(√2)²
)
+2√6 =
-(
(√3)²+2√3*√2 +(√2)²
)/
(3-2) +2√6 =-(3+2√6 +2) +2√6 = -5 -2√6 +2√6 = -
5.
*********************************************************
√(12+6√3)
=
√(9+2*3*√3 +3)
=√(3² +2*3*√3+(√3)²) = √(3+√3)²
=3+√3.
√(11-6√2)
=
√(9 -2*3*√2 +2)
= √(3² -2*3*√2 +(√2)² ) = √(3-√2)²
=3 -√2
.
числитель : √(12+6√3) -√(11-6√2) =(3+√3) -(3 -√2) =√3+√2 .
2 votes
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Answers & Comments
Verified answer
( √(12+6√3) - √(11-6√2) ) /(√2 -√3) + √24 =( (3+√3) -(3-√2) ) / (√2 -√3) + √24 = - (√3 +√2) /(√3 -√2) +2√6 =
= - (√3 +√2)(√3 +√2( /(√3 -√2)(√3 +√2) +2√6 = -(√3+√2)² / ((√3)² -(√2)²) +2√6 =
-((√3)²+2√3*√2 +(√2)² )/ (3-2) +2√6 =-(3+2√6 +2) +2√6 = -5 -2√6 +2√6 = - 5.
*********************************************************
√(12+6√3) =√(9+2*3*√3 +3) =√(3² +2*3*√3+(√3)²) = √(3+√3)² =3+√3.
√(11-6√2) = √(9 -2*3*√2 +2) = √(3² -2*3*√2 +(√2)² ) = √(3-√2)² =3 -√2 .
числитель : √(12+6√3) -√(11-6√2) =(3+√3) -(3 -√2) =√3+√2 .