Question

[Phanh Cobis]

So sánh 10⁵⁰+1/10⁵⁰-3  với 10⁵⁰+3/10⁵⁰-1

Giúp mình với mình tick cho

Answer 1

[Jaki Nastumi]

\(\frac{10^{50}+1}{10^{50}-3}=\frac{\left(10^{50}-3\right)+4}{10^{50}-3}=1+\frac{4}{10^{50}-3}\)

\(\frac{10^{50}+3}{10^{50}-1}=\frac{\left(10^{50}-1\right)+4}{10^{50}-1}=1+\frac{4}{10^{50}-1}\)

Ta so sánh \(\frac{4}{10^{50}-3}với\frac{4}{10^{50}-1}\) . Ta có \(\frac{4}{10^{50}-3}\)  > \(\frac{4}{10^{50}-1}\)     => 10⁵⁰+1/10⁵⁰-3  > 10⁵⁰+3/10⁵⁰-1

Answer 2

[Arima Kousei]

Ta có :  

\(\frac{10^{50}+1}{10^{50}-3}=\frac{10^{50}-3+4}{10^{50}-3}=1+\frac{4}{10^{50}-3}\)

\(\frac{10^{50}+3}{10^{50}-1}=\frac{10^{50}-1+4}{10^{50}-1}=1+\frac{4}{10^{50}-1}\)

Do \(\frac{4}{10^{50}-3}>\frac{4}{10^{50}-1}\)

\(\Rightarrow1+\frac{4}{10^{50}-3}>1+\frac{4}{10^{50}-1}\)

\(\Rightarrow\frac{10^{50}+1}{10^{50}-3}>\frac{10^{50}+3}{10^{50}-1}\)

Chúc bạn học tốt !!!