Question

Calculati folosind formulele de calcul prescurtat: a) (3-√2)² ; (2-√3)² ; (4+√2)² ; b) (4-√3)² ; (5-√2)² ; (√5+√3)² ; c) (√5-√2)² ; (√5+√7)² ; (√3+2)² ; d) (3-√5)² ; (√3-√2)² ; (√6+2)² ; e) (√6-3)² ; (√5-√6)² ; (2√3-1)² ; g) (√6-√3) (√6+√3)-(√6-√10) (√6+√10).

Answer 1

a)
(3-√2)² = 3² - 2×3×√2+2 = 9 + 2 - 6√2 = 11 - 6√2

→ aplic formula ( a - b)² = a² - 2ab+b²

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(2-√3)²= 2² - 2×2√3 + (-√3)² = 4 - 4√3+3 = 7 - 4√3

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(4+√2)² = 4²+2×4√2 + (√2)² = 16+8√2+2 = 18+8√2

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b)
(4-√3)² = 4² - 2×4√3 + (-√3)² = 16 - 8√3+3 = 19 - 8√3

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 (5-√2)² = 5² - 2×5√2 + 2 = 25+2 - 10√2 = 27 - 10√2

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(√5+√3)² = (√5)² +2×√5×√3 + (√3)² = 5+2√15+3 = 8+2√15

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 c)
(√5-√2)² =(√5)² - 2×√5×√2 +√2² = 5+2 - 2√10 = 7 - 2√10

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(√5+√7)² = (√5)² + 2×√5×√7 + (√7)² = 5+2√35+7 = 12+2√35

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 (√3+2)² = (√3)² + 2×2√3 + 2² = 3+4+4√3 = 7+4√3

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 d)
 (3-√5)² = 3² - 2×3√5 + √5² = 9+5-6√5 = 14 - 6√5

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 (√3-√2)²= (√3)² - 2×√3×√2 + √2² = 3+2 - 2√6 = 5 - 2√6

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(√6+2)² = (√6)² + 2×2√6 + 2² = 6+4 + 4√6 = 10 + 4√6

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e)
(√6-3)² = (√6)² - 2×3√6 + 3² = 6+9 - 6√6 = 15 - 6√6

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 (√5-√6)² = (√5)² - 2×√5×√6 + (-√6)² = 5+6 - 2√30 = 11 - 2√30

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 (2√3-1)² = (2√3)² - 2×2√3×1 + (-1)² = 4×3-4√3+1 = 13 - 4√3

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 g)
(√6-√3) (√6+√3)-(√6-√10) (√6+√10)= (6-3) - (6-10) = 3 - (-4) = 3+4=7

aplic formula ( a-b)(a+b) = a²-b²

sau:

= √36 - √18 + √18 -√9 - (√36-√60+√60-√100) =

= 6 - 3 - (6-10) =

= 3 - (-4) =

= 3 +4 =

= 7

Answer 2

a)(3-√2)^2=9-6√2+2=11-6√2
(2-√3)^2=4-4√3+3=7-4√3
(4+√2)^2=16+8√2+2=18+8√2
b)(4-√3)^2=16-8√3+3=19-8√3
(5-√2)^2=25-10√2+2=27-10√2
(√5+√3)^2=5+2√15+3=8+2√15
c)(√5-√2)^2=5-2√10+2=7-2√10
(√5+√7)^2=5+2√35+7=12+2√35
(√3+2)^2=3+4√3+4=7+4√3
d)(3-√5)^2=9-6√5+5=14-6√5.
(√3-√2)^2=3-2√6+2=5-2√6
(√6+2)^2=6+4√6+4=10+4√6
e)(√6-3)^2=6-6√6+9=15-6√6
(√5-√6)^2=5-2√30+6=11-2√30
(2√3-1)^2=12-4√3+1=13-4√3
g)(√6^2-√3^2)(√6^2-√10^2)=
3×(-4)=-12