Find the integer x that satisfies the equation x5−101x3−999x2+100900=0.
Answer:
10
- We need to find the integer value of x that satisfies the equation x5−101x3−999x2+100900=0.
- x5−101x3−999x2+100900=0⟹x5−101x3−999x2+100899+1=0⟹x3(x2−101)−999(x2−101)+1=0⟹(x2−101)(x3−999)+1=0…(1)
- We observe that the only integer that satisfies (1) is 10.
Hence, the value of x is 10.