If x is a positive integer less than 100, how many value of x make 1+2+3+4+x an integer?
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It is 7 do you need process?
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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
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