Question

N is an integer and 3^90 is between N and N+1. Find the value of N.

Answer 1

Answer:

[tex]To find the minimum value of n!(21−n)!=21!21!n!(21−n)!=21!21Cn1=21Cn21!

For minimum value, 21Cn is maximum.

Maximum value of 21Cn=221C21−1=21C10

∴ Minimum value =21C1021!=21!21!×10!11!=10!11!  

According to the example.

Answer 2

Answer:

N = 4

Step-by-step explanation:

4³ = 64 and 5³ = 125

64 < 90 < 125 and so

³√64<³√90<³√125

So 4< ³√90 <5 and N = 4