Question

Daca a supra 0,6 = b supra 0.9 , atunci rezultatul calculului : (b supra a)^0 + (b supra a )^-1 + (b supra a )^-2 cu cat este egal? Multumesc frumos!!!

Answer 1

Răspuns: $\bf \dfrac{19}{4}$

Explicație pas cu pas:

Buna!

$\bf \dfrac{a}{0,6} =\dfrac{b}{0,9} \implies 0,6\cdot b=0,9\cdot a\implies \dfrac{b}{a}=\dfrac{0,6}{0,9}$

$\bf \implies \dfrac{b}{a}=\dfrac{\dfrac{6}{10}}{\dfrac{9}{10}}= \dfrac{6}{10}\cdot\dfrac{10}{9} = \dfrac{\not6}{\not10}\cdot\dfrac{\not10}{\not9}\implies \boxed{\bf \dfrac{b}{a}=\dfrac{2}{3}}$

$\bf \bigg(\dfrac{2}{3} \bigg)^{0}+\bigg(\dfrac{2}{3} \bigg)^{-1}+\bigg(\dfrac{2}{3} \bigg)^{-2}=$

$\bf 1+\dfrac{3}{2} +\bigg(\dfrac{3}{2} \bigg)^{2}=$

$\bf 1+\dfrac{3}{2} +\dfrac{9}{4}=$

$\bf \dfrac{4}{4} +\dfrac{3 \cdot 2}{2 \cdot 2} +\dfrac{9}{4}=$

$\bf \dfrac{4+6+9}{4}=$

$\boxed{\boxed{\bf \dfrac{19}{4}}}$

Bafta multa!