Aratati ca urmatoarele nr. sunt patrate perfecte​

Răspuns:

Explicație pas cu pas:

b)

32 (93 - 85) = 32*8 = 2^5 * 2^3 = 2^8 = (2^4)^2 patrat perfect

c)

2^83 - 2^82 = 2^82 (2 - 1) = 2^82 = (2^41)^2 patrat perfect

d)

5^21 - 5^20 - 5^18 = 5^18 (5^3 - 5^2 - 1) = 5^18 (125 - 25 - 1) = 99*5^18

11 * 99 * 5^18 = 11 * 11 * 9 * 5^18 = 11^2 * 3^2 *(5^9)^2 = (11*3*5^9)^2 patrat perfect

Răspuns:

Explicație pas cu pas:

b) 32 x 93 - 32 x 85 = 32 x ( 93 - 85 ) = 32 x 8 = 2⁵ x 2³ = 2⁸ =

= (2⁴)² = 16² => patrat perfect

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c) 2⁸³ - 4⁴¹ = 2⁸³ - (2²)⁴¹ = 2⁸³ - 2⁸² = 2⁸² x ( 2 - 1 ) = (2⁴¹)² =>patrat pefect

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d)

11 x ( 5²¹ - 5²⁰ - 5¹⁸ ) =

= 11 x 5¹⁸ x ( 5³ - 5² - 1 ) =

= 11 x (5⁹)² x ( 125 - 25 - 1 ) =

= 11 x (5⁹)² x 99 =

= 11 x ( 5⁹ )² x ( 11 x 9 ) =

= 11² x (5⁹)² x 3² =

= ( 3 x 5⁹ x 11 )² => patrat perfect