Question

stabiliți dacă următoarele numere sunt pătrate perfecte 9^15 b)4^7c)4^101)d)25^2001,e)16^35×9^25,f)4^5×49^11,g)3^6+3^7,,h)5^7+4×5^6,i)3^5+3^6-8×3^4,j)2^11+2^12,k)3^45-3^44-3^44-3^45443, l)2^55-2^54-2^53,m)5^21-5^20

Answer 1

a) 9¹⁵=(3²)¹⁵= (3¹⁵)²
b) 4⁷=(2²)⁷=(2⁷)²
c) 4¹⁰¹= (2²)¹⁰¹= (2¹⁰¹)²
d)25²⁰⁰¹= (5²)²⁰⁰¹= (5²⁰⁰¹)²
e)e)16³⁵×9²⁵= (2⁴)³⁵* (3²)²⁵=2¹⁴⁰*3⁵⁰= (2⁷⁰*3²⁵)²
f)4⁵*49¹¹=( 2⁵)²*(7¹¹)²= (2⁵*7¹¹)²
g)3⁶+3⁷=3⁶*(1+3)= 3⁶*4= (3³*2)²
h)5⁷+4*5⁶= 5⁶*(5+4)=5⁶*9= (5³*3)²
i)3⁵+3⁶-8*3⁴=3⁴*(3+3²-8)=3⁴*(12-8)=3⁴*4=(3²*2)²
j)2¹¹+2¹²=2¹¹ *(1+2)⁼ 2¹¹*3=2048×3=6144
 (nu este patrat perfect.)
k)3⁴⁵-3⁴⁴-3⁴⁴-3⁴⁵+3⁴³= 3⁴³*(3²-3-3-3²+1)= 3⁴³*((9-3-3-9+1)=3⁴³*(-5) (nu este patrat perfect)
l) 2⁵⁵-2⁵⁴-2⁵³=2⁵³*(2²-2-1)=2⁵³*(4-2-1)=2⁵³(nu este patrat perfect)
m) 5²¹-5²⁰=5²⁰*(5-1)= 5²⁰*4=( 5¹⁰*2)²