Question

ex 1, toate punctele! va rog. dau coroana ​

Answer 1

Răspuns:

Explicație pas cu pas:

a)

$a=\frac{12}{\sqrt{6}} + \sqrt{(1-\sqrt{6})^2} + |-1| =$

$=\frac{12*\sqrt{6} }{\sqrt{6}*\sqrt{6} } + |(1-\sqrt{6}| +1 =$

$=\frac{12*\sqrt{6} }{6 } + \sqrt{6}-1 + 1 =$

$=2*\sqrt{6} + \sqrt{6} =$

$=3*\sqrt{6}$

$b = |2-\sqrt{12}|+2*\sqrt{(-1+\sqrt{3}-3*\sqrt{6} )^2} =$

$= \sqrt{12}-2 +2*|-1+\sqrt{3}-3*\sqrt{6}| =$

$= \sqrt{4*3}-2 +2*(1-\sqrt{3}+3*\sqrt{6}) =$

$= \sqrt{4}*\sqrt{3} -2 +2-2*\sqrt{3}+6*\sqrt{6} =$

$= 2*\sqrt{3}-2*\sqrt{3}+6*\sqrt{6} =$

$= 6*\sqrt{6}$

m=min{a;b} = min(3√6 ; 6√6) = 3√6 = a

M=max{a;b} = max(3√6 ; 6√6) = 6√6 = b

b)

$ma = \frac{a+b}{2} = \frac{3*\sqrt{3}+6*\sqrt{3} }{2} = \frac{\sqrt{3}*(3+6) }{2} = \frac{9*\sqrt{3}}{2} =4,5*\sqrt{3}$

$mg = \sqrt{a*b} = \sqrt{3*\sqrt{3} *6*\sqrt{3} } = \sqrt{3*6*\sqrt{3}*\sqrt{3} }=$

$= \sqrt{3*6*3 } = \sqrt{3*3}*\sqrt{6} = 3*\sqrt{6}$

Asadar:

m = mg = $3*\sqrt{6}$ <$4,5*\sqrt{6}$ = ma < $6*\sqrt{6}$ = M

Deci

m ≤ mg ≤ma ≤M.