Răspuns:
Explicație pas cu pas:
1.a.
[tex]a=2^{n+14}:2^{14}+5^{2n}: 5^{2n}=2^{n}+1[/tex]
[tex]b=\frac{5^{2}*5^{n}*2^{n}+2^{n}*11^{n}*11 }{11^{n+1}+5^{n+2} } =\frac{2^{n}(5^{n+2}+11^{n+1} ) }{5^{n+2}+11^{n+1} }=2^{n}[/tex]
[tex]c=2^{n}(4-2-1)-1 =2^{n}-1[/tex]
b.
[tex]\frac{a+c}{2}=\frac{2^{n}+1+2^{n}-1 }{2}=\frac{2^{n+1} }{2} =2^{n}=b[/tex]
2.
a.
[tex](a+a\frac{x}{100} )-(a+a\frac{x}{100} )*\frac{x}{100} =a-a\frac{4}{100}[/tex]
[tex]a+\frac{ax}{100}- \frac{ax}{100}-\frac{ax^{2} }{10000} =\frac{96a}{100}[/tex]
[tex]a-\frac{ax^{2} }{10000} =\frac{96a}{100}[/tex]
[tex]10000a-ax^{2} -9600a=0\\400a-ax^{2} =0\\a(400-x^{2} )=0\\x^{2} =400, x=20[/tex]
b.
[tex]24=2^{3}*3\\ 40=2^{3}*5\\ 56=2^{3}*7\\ cmmmc=2^{3}*3*5*7=840[/tex]
a=b*840+4, cel mai mic este pentru b=1,
a=844
