G.2145
a*0.(3) = b * 0.(6) => 3a/9 = 6b/9 => a/3 = 2b/3 => a=2b
2a+3b = 24
4b+3b = 24 => 7b = 24 = > b= 24/7 ; a= 48/7
G.2152
a. 4044121 = 2011² deci e patrat perfect
b. 20102011 = 433 * 45377 deci nu e patrat perfect
20112012 = 2² * 3² * 421 * 1 327 deci nu e patrat perfect
G.2156
12n! = (n+2)! => 12n! = n! * (n+1) * (n+2)
12= (n+1)(n+2)
n²+2n+n+2 =12
n²+3n-10=0
Δ= 3² - 4* (-10) *1 = 49 => √Δ=7
n1= (-3 + 7)/2 = 2 ∈ N
n2= (-3 - 7)/2 = -5 ∉ N
=> solutia este n =2
