Page 84 - math 12

R ﻲﻓ ٍﺪﺣﺍﻭ ﺮﻴﻐﺘﻤﺑ ِﺔﻴﻧﺎﺜﻟﺍ ِﺔﺟﺭﺪﻟﺍ ﻦﻣ ٍﺕﻻﺩﺎﻌﻣ ﻞَﺣ ُ ﺱﺭﺪﻟﺍ
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ﱡ
Solving Second Degree Equations with One Variable in R [4-3]

ﱠ
ﻢﻠَﻌَﺗ ﺱﺭﺪﻟﺍ ُﺓﺮﻜﻓ
ِ
ﻲﻓ
ﺏﺮﻏ
َ
ﻊﻘﻳ
ﺝﺮﺑ

َ ﺏﺮﻏ ﻙﻮﻣﺮﻴﻟﺍ ﺔﻘﻄﻨﻣ ﻲﻓ َﺩﺍﺪﻐﺑ ُﺝﺮﺑ ُﻊﻘﻳ ﺔﺟﺭﺪﻟﺍ ﻦﻣ ﺔﻟﺩﺎﻌﻣ ﻞﺣ
ﻙﻮﻣﺮﻴﻟﺍ
ﺔﻘﻄﻨﻣ
ُ
َ
ّ
ﺩﺍﺪﻐﺑ ُ
.R ﻲﻓ ٍﺪﺣﺍﻭ ﺮﻴﻐﺘﻤﺑ ﺔﻴﻧﺎﺜﻟﺍ
ٍ

ﻎﻠﺒﻳﻭ
ﻪﻋﺎﻔﺗﺭﺍ
ﻪﻋﺎﻔﺗﺭﺍ ﻎﻠﺒﻳﻭ 1991 ﺔﻨﺳ ﻲﻨُﺑﻭ َﺩﺍﺪﻐﺑ
ﺕﺍﺩﺮﻔﻤﻟﺍ
ُُ
ﺔﻌﺑﺮﻤﻟﺍ ﺝﺮﺒﻟﺍ ِﺓﺪﻋﺎﻗ ﺔﺣﺎﺴﻣﻭ ، ٌ
ﺔﻌﺑﺮﻤﻟﺍ ﺝﺮﺒﻟﺍ ِﺓﺪﻋﺎﻗ ﺔﺣﺎﺴﻣﻭ ،204m .ِﺔﻴﻧﺎﺜﻟﺍ ِﺔﺟﺭﺪﻟﺍ ﻦﻣ ﺔﻟﺩﺎﻌﻣ
ِِ
ُ
.ﻱﺮﻔﺼﻟﺍ ِﺏﺮﻀﻟﺍ ﺔﻴﺻﺎﺧ
. ﺝﺮﺒﻟﺍ ِﺓﺪﻋﺎﻗ ﻊﻠﺿ ﻝﻮﻁ ْﺪﺟ ،36m 2
َ
ِ
ِ
ﻲﻌﻴﺑﺮﺘﻟﺍ ﺭﺬﺠﻟﺍ ﻝﺎﻤﻌﺘﺳﺎﺑ ِﺕﻻﺩﺎﻌﻤﻟﺍ ﻞﺣ [4-3-1]
ﱢ
ّ
ِ
Solving the Equations by Using Square Root
ُ
ُ
، ﺔﻴﻧﺎﺜﻟﺍ ﺓﻮﻘﻟﺍ ﻲﻫ ﺮﻴﻐﺘﻤﻠﻟ ٍﺓﻮﻗ ﺮﺒﻛﺃ ﺎﻬﻴﻓ ﻲﺘﻟﺍ ﺔﻟﺩﺎﻌﻤﻟﺍ ﻲﻫ ٍﺪﺣﺍﻭ ﺮﻴﻐﺘﻤﺑ ﺔﻴﻧﺎﺜﻟﺍ ﺔﺟﺭﺪﻟﺍ ﻦﻣ ﺔﻟﺩﺎﻌﻤﻟﺍ
ٍ
ِ
. x ﺮﻴﻐﺘﻤﻠﻟ ﻦﻴﺘﻤﻴﻗ ﺩﺎﺠﻳﺍ ﻲﻨﻌﻳ ﺎﻬﻠﺣﻭ ،14x – 2x = 0 ، x = 25 ًﻼﺜﻣ
2
2
ُ
.ِﺓﺪﻋﺎﻘﻟﺍ ﻊﻠﺿ ﻝﻮﻁ ْﺪﺟ ،36m ﻮﻫ ﺝﺮﺒﻟﺍ ِﺓﺪﻋﺎﻗ ﺔﺣﺎﺴﻣ (1) ﻝﺎﺜﻣ
2
َ
ِ
ِ
2
x = 36 ﻲﻫ ﺓﺪﻋﺎﻘﻟﺍ ﺔﺣﺎﺴﻣ ﻞﺜﻤﺗ ﻲﺘﻟﺍ ﺔﻟﺩﺎﻌﻤﻟﺍ
x = 36 ﻭﺃ x = - 36 36 ﺩﺪﻌﻠﻟ ﻥﺎﻴﻌﻴﺑﺮﺗ ﻥﺍﺭﺬﺟ ﺪﺟﻮﻳ
x = 6 ﻭﺃ x = - 6 36 ﺩﺪﻌﻟﺍ ﺍﺭﺬﺟ ﺎﻤﻫ - 6 ﻭ 6
، 6m ﻮﻫ ﺝﺮﺒﻟﺍ ﺓﺪﻋﺎﻗ ﻊﻠﺿ ﻝﻮﻁ ﺍﺬﻟ
. ًﺎﺒﻟﺎﺳ ﻥﻮﻜﻳ ﻥﺍ ﻦﻜﻤﻳﻻ ِﺓﺪﻋﺎﻘﻟﺍ ﻝﻮﻁ ﱠﻥﻻ ﻞﻤﻬُﺗ x = - 6 ﺔﻤﻴﻘﻟﺍﻭ
َ
ُ
: ﻲﻌﻴﺑﺮﺘﻟﺍ ﺭﺬﺠﻟﺍ ﻝﺎﻤﻌﺘﺳﺎﺑ ﺔﻴﻟﺎﺘﻟﺍ ِﺕﻻﺩﺎﻌﻤﻟﺍ ﻞﺣ (2) ﻝﺎﺜﻣ
ﱢ
ِ
ﱠ
i) y = 32 ⇒ y = 32 ﻭﺃ y = - 32 ⇒ y = 4 2 ﻭﺃ y = - 4 2
2
1
ii) 16 z = 4 ⇒ 1 ( 16z ) = 1 × 4 ⇒ z =
2
2
2
16 16 4
1 1 1 1
⇒ z = z = - ⇒ z = z = -
ﻭﺃ
ﻭﺃ
4 4 2 2
1
1
1
iii) 8 x = 1 ⇒ (8x ) = × 1 ⇒ x = ⇒ x = 1 ﻭﺃ x = - 1
2
2
2
8 8 8 8 8
1 1 1 1
⇒ x = ﻭﺃ x = - ⇒ x = ﻭﺃ x = -
8 8 2 2 2 2
iv) t – 1 = 11 ⇒ t = 12 ⇒ t = 12 ﻭﺃ t = - 12 ⇒ t = 2 3 ﻭﺃ t = - 2 3

2
2
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