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Algebra Level 3

Consider all integers x x such that 9 < x 2 < 99 9< { x }^{ 2 }<99 . Find max ⁡ ( x ) − min ⁡ ( x ) . \max(x) - \min(x) .

5 0 18 8 -8 13

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Dinesh Nath Goswami by Dinesh Nath Goswami , 20, India

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3 solutions 

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The only squares sandwiched between 9 and 99 are:
16, 25, 36, 49, 64, 81

Square roots:
+/- 4,5,6,7,8,9
( x can be a positive or negative integer. It was not specified in the question. )

max = + 9
min = -9

9-(-9) = 18

13 Helpful 0 Interesting 0 Brilliant 0 Confused

Can you tell how to spot 9 and -9 without moving and doing trail and error.

Syed Baqir - 5 years, 9 months ago
Aryan Gaikwad
Aug 25, 2015

Max value of x = 9 x = 9 . Min value = − 9 =-9

6 Helpful 0 Interesting 0 Brilliant 0 Confused

Can you elaborate your method more please ?

Syed Baqir - 5 years, 9 months ago

I agree with Syed; this literally did not answer anything.

Andy Wong - 5 years, 6 months ago
Hadia Qadir
Aug 30, 2015

9 < x^2 < 99
-sqrt (99) < x < sqrt(99)
-9,... < x < 9,....
the min of x is -9 and the max is 9
the diff = 18



0 Helpful 0 Interesting 0 Brilliant 0 Confused

It will be best if you use Latex or spaces between two lines

Syed Baqir - 5 years, 9 months ago

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