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30121999
@30121999
October 2021
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8
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Срочно помогает! Алимов 8 класс! Проверь себя на странице 157, 2 уровень!
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m11m
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7. a) 4,6 и √22 б) 2√37 и 5√6
√4,6² и √22 √4*37 и √25*6
√21,16 и √22 √148 и √150
√21,16 < √22 √148 < √150
4.6 <√22 2√37 < 5√6
8
. а) (5√3 - √15) / √5 - 1 = [(5√3 - √15) / (√5 - 1)] * [(√5 +1)/(√5 + 1)]=
=(5√15 - √75 +5√3 - √15) / (5-1)=
=(5√15 - √15 + 5√3 - 5√3) / 4= (4√15) / 4=√15
б) (√27 + √12 + 5) (1-√3)=
=√27 + √12 + 5 - √27*3 - √12*3 - 5√3 =
=√9*3 + √4*3 + 5 - √81 - √36 - 5√3 =
=3√3 + 2√3 + 5 - 9 - 6 - 5√3 =
=5√3 - 5√3 - 10= - 10
в) (2√6 - 3√3) / (1 - √2)² = (2√3 * √2 - 3√3) / (1 - 2√2 +2)=
=(√3 (2√2 - 3)) / (3 - 2√2) = -(√3 (3 - 2√2)) / (3 - 2√2)= -√3
г) (√4(х-у)²) / (х-у)=
=(4(х-у)) / (х-у) =
=4
9. ху²√х/у³ = √х²ху⁴/у³ = √х³у
10.
1-2√х+х
= -
(1-√х)
²
= -
(1-√х)(1-√х)
= -
(1-√х)(1-√х)
=-
(1-√х)
х-1 1-х 1²-(√х)² (1-√х)(1+√х) 1+√х
=
√х - 1
1+√х
11.
√2+1
=
√2+1
*
√2+1
=
(√2+1)²
=
2+2√2+1
= 3+2√2
√2-1 √2-1 √2+1 2-1 1
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Answers & Comments
Verified answer
7. a) 4,6 и √22 б) 2√37 и 5√6√4,6² и √22 √4*37 и √25*6
√21,16 и √22 √148 и √150
√21,16 < √22 √148 < √150
4.6 <√22 2√37 < 5√6
8. а) (5√3 - √15) / √5 - 1 = [(5√3 - √15) / (√5 - 1)] * [(√5 +1)/(√5 + 1)]=
=(5√15 - √75 +5√3 - √15) / (5-1)=
=(5√15 - √15 + 5√3 - 5√3) / 4= (4√15) / 4=√15
б) (√27 + √12 + 5) (1-√3)=
=√27 + √12 + 5 - √27*3 - √12*3 - 5√3 =
=√9*3 + √4*3 + 5 - √81 - √36 - 5√3 =
=3√3 + 2√3 + 5 - 9 - 6 - 5√3 =
=5√3 - 5√3 - 10= - 10
в) (2√6 - 3√3) / (1 - √2)² = (2√3 * √2 - 3√3) / (1 - 2√2 +2)=
=(√3 (2√2 - 3)) / (3 - 2√2) = -(√3 (3 - 2√2)) / (3 - 2√2)= -√3
г) (√4(х-у)²) / (х-у)=
=(4(х-у)) / (х-у) =
=4
9. ху²√х/у³ = √х²ху⁴/у³ = √х³у
10. 1-2√х+х = - (1-√х)² = - (1-√х)(1-√х) = -(1-√х)(1-√х) =- (1-√х)
х-1 1-х 1²-(√х)² (1-√х)(1+√х) 1+√х
=√х - 1
1+√х
11. √2+1 = √2+1 * √2+1 = (√2+1)² =2+2√2+1 = 3+2√2
√2-1 √2-1 √2+1 2-1 1