Question

Q. What is the greatest positive integer n which makes n³+100 divisible by n+10.​

Answer 1

Answer:

n = 890

Step-by-step explanation:

---> For [ n + 10 ] to divide [ n³ + 100 ], let's follow the steps :->

--> Firstly, --> a | b, means that a completely divides b without leaving any remainder...

Now, --> [ n + 10 ] | [ n³ + 100 ]

======> [ n + 10 ] | [ n³ + 1000 ] - 900 ---> ( a + b ) | ( a³ + b³ )

======> [ n + 10 ] | -900

Hence, biggest no. for which [ n + 10 ] divides -900 is :->

---> [ n + 10 ] = 900

---> n = 890..

VERIFICATION :->

---> [ 890 + 10 ] = 900

---> [ 890 ]³ + 100 = 704969000 + 100 = 704969100

Clearly, 900 * 783299 = 704969100..

Hence, your req.d answer is 890...