Fie numerelex si y cu proprietatile: X-9=8x(9+9²+9³+......+9ⁿ⁻¹)si Y-12=4x(5+5²+5³+.........+5ⁿ).Sa se demonstreze ca X este patrat perfect ,iar Y nu este patrat perfect

Răspunsul a fost dat de: USER1744
29 Agustus 2025 matematica 5 minute
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Clasă: Education Materie: matematica
Fie numerelex si y cu proprietatile: X-9=8x(9+9²+9³+......+9ⁿ⁻¹)si Y-12=4x(5+5²+5³+.........+5ⁿ).Sa se demonstreze ca X este patrat perfect ,iar Y nu este patrat perfect
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X-9=9 (9^(n-1)-1) X=(3^n)^2 este p.p ptr orice n ap lui N Y-12=4x5x(5^n-1)/4=5^(n+1)-5 Y=5^(n+1)+7 nu este pătrat perfect ptr orice n ap lui N
Răspunsul a fost dat în data 29 Agustus 2025

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