РЕШЕНИЕ:
√720 ⋅ √240 = √360 ⋅ √240 = √(36∙10∙10∙4∙6) = 120√6
√2
Ответ: 120√6

РЕШЕНИЕ:

1/4 x²​ − 36=0

x² = 36 ∙ 4/1

x² = 144

х = ± 12

Ответ: − 12

РЕШЕНИЕ:



KB = AB/2 = 13/2 = 6.5

∆ AMD ∞ ∆ BMC

BM : AM = BC : AD

x : (13+x) = 24 : 48

48x = 24(13+x)

48x – 24x = 312

24x = 312

x = 13 = BM

R = BM + KB = 13 + 6.5 = 19.5

Ответ: 19.5

РЕШЕНИЕ:



S∆ABK + S∆AKM = S∆ / 2 ⇒ S∆ABK = S∆ / 2 – S∆AKM

BK:KM=2:7 ⇒
S∆ABK = 2
S∆AKM__7

S∆ / 2 – S∆AKM = 2
S∆AKM__7

7S∆ – 14 S∆AKM = 4 S∆AKM

18 S∆AKM = 7S∆

S∆AKM = 7S∆ / 18

∆AKM ∞ ∆NKB

AM = KM
BN__BK

x = 7
BN__2

BN = 2x / 7

∆ACP ∞ ∆NBP

AC = PC
BN__BP

2x__ = PC
2x / 7__BP

7 = PC
1 __BP

S∆ABP = BP
S∆APC__PC

S∆ABP = 1
S∆APC__7

S∆ABP + S∆APC = S∆ ⇒ S∆ABP = S∆ – S∆APC

S∆ – S∆APC = 1
S∆APC______7

7 S∆ – 7 S∆APC = 1 S∆APC

8 S∆APC = 7 S∆

S∆APC = 7 S∆ / 8

S KPCM = S∆APC – S∆AKM = 7 S∆ / 8 – 7S∆ / 18 = 35S∆ / 72

S∆ABK = S∆/2 – S∆AKM = S∆/2 – 7S∆ / 18 = 2S∆ / 18 = S∆ / 9

S∆ABK / S KPCM = S∆ / 9 : 35S∆ / 72 = 1/9 ∙ 72/35 = 8/35

Ответ: 8/35