Question

So sánh :

a) \(\left(\frac{1}{243}\right)^9\) và \(\left(\frac{1}{83}\right)^{13}\)

b)1990^10+1990^9 và 1991^10

Answer 1

a) \(\left(\frac{1}{243}\right)^9=\left(\frac{1}{3^5}\right)^9=\frac{1}{3^{45}}\)

\(\left(\frac{1}{83}\right)^{13}< \left(\frac{1}{81}\right)^{13}=\left(\frac{1}{3^4}\right)^{13}=\frac{1}{3^{52}}< \frac{1}{3^{45}}=\left(\frac{1}{243}\right)^9\Rightarrow\left(\frac{1}{83}\right)^{13}< \left(\frac{1}{243}\right)^9\)

b) 1990¹⁰ + 1990⁹

= 1990⁹ ( 1990 + 1 )

= 1990⁹ . 1991 < 1991¹⁰ = 1991⁹ . 1991

Vậy 1990¹⁰ + 1990⁹ < 1991¹⁰