Răspuns:
la b nu se intelege prea bine, presupun ca a doua putere a lui 2 este 10
Explicație pas cu pas:
a)
[tex]x=19*9 + 19*10 = 19*(9+10)=19*19 = 19^2[/tex]
[tex]\sqrt{x} = \sqrt{(19^2)} = 19[/tex]
b)
[tex]x = 2^{11} - 2^{10} = 2^{1+10} - 2^{10} = 2*2^{10} - 2^{10} = 2^{10}*(2-1)=2^{10}= (2^5)^2[/tex]
[tex]\sqrt{x} =\sqrt{[(2^5)^2]}=2^5 =32[/tex]
c)
[tex]x= 200+199*200 = 200*(1 + 199) = 200*200=200^2[/tex]
[tex]\sqrt{x} = \sqrt{(200^2)} = 200[/tex]
d)
[tex]x= n+n*(n-1) = n + n^2 - n = n^2[/tex]
[tex]\sqrt{x} = \sqrt{(n^2)} =n[/tex]
e)
[tex]x= \sqrt{441}+\sqrt{\frac{42*43+43*44}{2}} = \sqrt{(221^2)}+\sqrt{\frac{43*(42+44)}{2}} = 221+\sqrt{\frac{43*86}{2}} = 221+\sqrt{43*43} = 221+\sqrt{(43^2)} = 221+43=264[/tex]
f)
[tex]x=\frac{3^{n+2}-3^{n+1}-2*3^n}{3^n} =\frac{3^n*(3^2-3^1-2)}{3^n} = 9-3-2 = 6-2 = 2 = 2^2[/tex]
[tex]\sqrt{x} = \sqrt{(2^2)} =2[/tex]
