Question

Arătați că nr a=(x • x² •x³ •.......x²°):(x •x³•x la puterea a 5a•…•x puterea 19) este pătrat perfect,oricare ar fi nr natural nenul x

Answer 1

$S_1=1+2+3+\ldots+20=\dfrac{(1+20)\cdot20}{2}=210;\\\\S_2=1+3+5+\ldots+19=\dfrac{(1+19)\cdot\left(1+\dfrac{19-1}{2}\right)}{2}=100;\\\\a=\dfrac{x^{S_1}}{x^{S_2}}=x^{S_1-S_2}=x^{210-100}=x^{110}=(x^{55})^2,\;care\;este\;p\breve{a}trat\;perfect.$

Green eyes.