Question

Exercitiu 3 si 5 va rog,dau review ,inimi, follow si coroana

Answer 1

3)

a)

3✓5+7✓5-2✓5 = (3+7-2)✓5 = 8✓5

b)

4✓2 + ( - ✓2) - ( - 3✓2) = 4✓2 - ✓ 2 + 3✓2=

= (4-1+3)✓2 = 6✓2

c) nu se vede tot

d)

4 - ( - ✓3) + (- 7✓3) - 1 = 4+✓3-7✓3 -1=

= 4 - 1 +( 1 - 7) ✓3 = 3 - 6✓3

e)

3✓10 - ( - 5✓2) - 4✓10 - ✓2 =

= 3✓10 - 4✓10 +5✓2 - ✓2 =

= (3-4)✓10 + (5-1)✓2 = - ✓10 + 4✓2

f) nu se vede tot

g)

${}^{4)} \frac{6 - 2 \sqrt{2} }{2} - \frac{3 \sqrt{2} - 5 }{8} = \\ \\ = \frac{24 - 8 \sqrt{2} - ( 3 \sqrt{2} - 5)}{8} = \\ \\ = \frac{24 - 8 \sqrt{2} - 3 \sqrt{2} + 5 }{8} = \\ \\ \frac{24 + 5 - 8 \sqrt{2} - 3 \sqrt{2} }{8} = \frac{29 - 11 \sqrt{2} }{8}$

h)

${}^{3)} \frac{2 \sqrt{3} - \sqrt{6} }{2} - \frac{ \sqrt{3} - 3 \sqrt{6} }{6} = \\ \\ = \frac{6 \sqrt{3} - 3 \sqrt{6} - ( \sqrt{3} - 3 \sqrt{6} ) }{6} = \\ \\ = \frac{6 \sqrt{3} - 3 \sqrt{6} - \sqrt{3} + 3 \sqrt{6} }{6} = \\ \\ = \frac{6 \sqrt{3} - \sqrt{3} - 3 \sqrt{6 } + 3 \sqrt{6} }{6} = \\ \\ = \frac{5 \sqrt{3} }{6}$

5)

a)

• 2✓8 - 5✓32 +4✓2=

✓8 = ✓ 2•2•2 = ✓ 2²•2 = 2✓2

✓32 = ✓ 4 • 8 = ✓ 2² • 2³ = ✓ 2² • 2² • 2 =

= 2•2✓2 = 4✓2

• = 2•2✓2 - 5•4✓2 +4✓2= 4✓2-20✓2+4✓2=

= (4-20+4)✓2 = -12 ✓ 2

b )

4✓3 + ✓ 12 = 4✓3 + ✓4•3= 4✓3+✓2²•3=

= 4✓3+2✓3 = 6✓3

c)

5✓2 +✓8 = 5✓2 +2✓2 = 7✓2