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Aratati ca nr. x este patrat perfect:
x=[2^30^2 •(2^6)^100•2+(64^4)^100:2^899]+2^3007

Răspuns :

[tex]x=[ 2^{ 30^{2} } \cdot (2^6)^1^0^0 \cdot 2+(64^4)^1^0^0:2^8^9^9]+2^3^0^0^7 \\ x=(2^9^0^0 \cdot 2^6^0^0 \cdot 2+64^4^0^0:2^8^9^9)+2^{3007} \\ x=[2^{900+600+1}+(2^6)^4^0^0:2^8^9^9]+2^{3007} \\ x=(2^{1501}+2^{2400}:2^8^9^9)+3^{3007} \\ x=(2^{1501}+2^{2400-899})+3^{3007} \\ x=(2^{1501}+2^{1501})+3^{3007} \\ x=(2 \cdot 2^{1501})^2+2^{3007} \\ x=2^{1502 \cdot 2}+2^{3007} \\ x=2^{3004}+2^{3007} \\ x=2^{3004}(1+2^3) \\ x=2^{3004}(1+8) \\ x=2^3^0^0^4 \cdot 9 [/tex]
[tex]x=2^{1502 \cdot 2 } \cdot 3^2 \\ x=(2^{1502} \cdot 3) ^2[/tex]