Question

Stabiliti daca urmatoarele numere sunt patrate perfecte:am sa scriu cu ghilimeme in locul puterii deoarece nu-mi merge tastatuta bine.a)9''15;b)4''7;c)64''25;d)25''2001;e)16''35x9''25;f)4''5x49''11;g)3''6+3''7;h)5''7+4x5''6;i)3''5+3''6-8x3''4;j)2''11+2''12;k)3''45-3''44-3''43;l)2''55-2''54-2''53;m)5''21x5''20.Va multumesc!

Answer 1

a)9^15 =3^30=(3^15)^2
b)4^7=2^14=(2^7)^2
c)64^25=8^50=(8^25)^2
d)25^2001=5^4002=(5^2001)^2
e)16^35x9^25=2^140 x 3^50=(2^70x3^25)^2
f)4^5x49^11=2^10x7^22=(2^5x7^11)^2
g)3^6+3^7=(3^3)^2x(3^0+3)=(3^3)^2x(1+3)=(3^3x2)^2
h)5^7+4x5^6=5^6(5^1+4x5^0)=5^6x(5+4)=5^6x9=(5^3x3)^2
i)3^5+3^6-8x3^4=3^4x(3^1+3^2-8x3^0)=3^4x(3+9-8)=3^4x4=(3^2x2)^2
de la a la i inclusiv sunt patrate perfecte
j)2^11+2^12=2^11(2^0+2)=2^11x3 nu este patrat perfect
k)3^45-3^44-3^43=3^43x(3^2-3^1-3^0)=3^43x(9-3-1)=3^43x5nu este patrat perfect
l)2^55-2^54-2^53=2^53x(2^2-2^1-2^0)=2^53x(4-2-1)=2^53 nu este patrat perfect
m)5^21x5^20=5^41 nu este patrat perfect