Question

Comparați nr.
A=3 la puterea 53 + 3 la puterea 52 +3 la puterea 51 și b=2 la puterea 87 +2 la puterea 86 +7×2la puterea 85

Answer 1

a = 3^53 + 3^52 + 3^51

a = 3^51 × (3^2 + 3^1 + 1)

a = 3^51 × ( 9 + 4)

a = 3^51 × 13
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b = 2^87 + 2^86 + 7 × 2^85

b = 2^85 × ( 2^2 + 2^1 + 7 × 1)

b = 2^85 × ( 4 + 2 + 7)

b = 2^85 × 13
__________


a = 3^51 × 13 = (3^3)^17 × 13 = 27^17 × 13

b = 2^85 × 13 = (2^5)^17 × 13 = 32^17 × 13

27 < 32 => 27^17 < 32^17 =>


=> 27^17 × 13 < 32^17 × 13 =>

=> a < b
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