Question

Aratati ca nr a este patrat perfect:
(x·x²·x³·....·xla puterea 20):(x·x la 3·x la 5·.....·xla 19)

Answer 1

$x \cdot x^2 \cdot x^3 \cdot ... \cdot x^{20}=x^{1+2+3+...20}= x^{ \frac{20 \cdot 21}{2} } = x^{210} . \\ \\ x \cdot x^3 \cdot x^5 \cdot ... \cdot x^{19}= x^{1+3+5+..+19}=x^{ \frac{(19 \cdot 1) \cdot 10}{2} }=x^{100}. \\ \\ a=x^{210}:x^{100}=x^{210-100}=x^{110}=(x^{55})^2-~patrat~perfect.$

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E din caietul de vacanta pentru clasa a saptea, nu?