Giải bài 84 trang 130 SGK giải tích nâng cao 12
So sánh p và q biết:
a) \({{\left( \dfrac{2}{3} \right)}^{p}}>{{\left( \dfrac{3}{2} \right)}^{-q}};\) b) \({{\left( \dfrac{8}{3} \right)}^{-p}}<{{\left( \dfrac{3}{8} \right)}^{q}};\)
c) \(0,{{25}^{p}}<{{\left( \dfrac{1}{2} \right)}^{2q}};\) d) \({{\left( \dfrac{7}{2} \right)}^{p}}<{{\left( \dfrac{2}{7} \right)}^{p-2q}}\).
a) \({{\left( \dfrac{2}{3} \right)}^{p}}>{{\left( \dfrac{3}{2} \right)}^{-q}}\Leftrightarrow {{\left( \dfrac{2}{3} \right)}^{p}}>{{\left( \dfrac{2}{3} \right)}^{q}} \)
Vì \(\dfrac{2}{3}<1\Rightarrow {{\left( \dfrac{2}{3} \right)}^{p}}>{{\left( \dfrac{2}{3} \right)}^{q}}\Leftrightarrow p< q \)
b) \({{\left( \dfrac{8}{3} \right)}^{-p}}<{{\left( \dfrac{3}{8} \right)}^{q}}\Leftrightarrow {{\left( \dfrac{3}{8} \right)}^{p}}<{{\left( \dfrac{3}{8} \right)}^{q}}\)
Vì \(\dfrac{3}{8}<1\Rightarrow {{\left( \dfrac{3}{8} \right)}^{p}}<{{\left( \dfrac{3}{8} \right)}^{q}}\Leftrightarrow p>q \)
c) \(0,{{25}^{p}}<{{\left( \dfrac{1}{2} \right)}^{2q}}\Leftrightarrow {{\left( \dfrac{1}{4} \right)}^{p}}<{{\left( \dfrac{1}{4} \right)}^{q}}\)
Vì \(\dfrac{1}{4}<1\Rightarrow {{\left( \dfrac{1}{4} \right)}^{p}}<{{\left( \dfrac{1}{4} \right)}^{q}}\Leftrightarrow p>q \)
d) \({{\left( \dfrac{7}{2} \right)}^{p}}<{{\left( \dfrac{2}{7} \right)}^{p-2q}}\Leftrightarrow {{\left( \dfrac{7}{2} \right)}^{p}}<{{\left( \dfrac{7}{2} \right)}^{2q-p}}\)
Vì \(\dfrac{7}{2}>1\Rightarrow {{\left( \dfrac{7}{2} \right)}^{p}}<{{\left( \dfrac{7}{2} \right)}^{2q-p}}\Leftrightarrow p<2q-p\Leftrightarrow p< q\)