Question

Arătați ca urmatoarele numere sunt patrate perfecte :
a) 2^21 +2^18
b) 3^24+3^25
c) 5^37-5^36

Answer 1

a ) 2²¹ + 2¹⁸ = 2¹⁸× ( 2³ + 1 ) = 2¹⁸ × ( 8 + 1) = 2¹⁸ × 9 = 2¹⁸ × 3² = ( 2⁹ × 3) ² → patrat perfect

b) 3 ²⁴ + 3 ²⁵ = 3 ²⁴ ( 1 + 3) = 3²⁴ x 4 = ( 3¹² ) ² x 2² = ( 3¹² x 2 ) ²

c) 5 ³⁷ - 5³⁶ = 5 ³⁶ ( 5 - 1 ) = ( 5¹⁸ ) ² x 4 = ( 5¹⁸ ) ² x 2² = ( 5¹⁸ x 2 ) ²