Question

If x is a positive integer less than 100 how many values of x make√1+2+3+4+x an integer?

Answer 1

x < 100
⇒x + 10 < 100 + 10
⇒ 1 + 2 + 3 + 4 + x < 110
⇒ √(1 + 2 + 3 + 4 + x ) = √(10 + x) < √110 < 11 ≤ 10
It means , value of square 0 < √(1 + 2 + 3 + 4 + x ) ≤ 10
at x = 6 , 15, 26, 39, 54 , 71 , 90
value of √(1 + 2 + 3 + 4 + x) will be integers
You can check ,by putting all values .

Hence, number of positive integer of x is 7

Answer 2

Answer:

x < 100

⇒x + 10 < 100 + 10

⇒ 1 + 2 + 3 + 4 + x < 110

⇒ √(1 + 2 + 3 + 4 + x ) = √(10 + x) < √110 < 11 ≤ 10

It means , value of square 0 < √(1 + 2 + 3 + 4 + x ) ≤ 10

at x = 6 , 15, 26, 39, 54 , 71 , 90

value of √(1 + 2 + 3 + 4 + x)

ANSWER 7

Step-by-step explanation: