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Algebra Level 4

If x x is an integer that satisfies the inequality

9 < x 2 < 99 , 9 < x ^2 < 99,

find the difference between the maximum and minimum possible values of x . x.

0 18 5 13 12 9 6

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Chung Kevin by Chung Kevin , 45, Australia

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6 solutions

Trevor Arashiro
Jan 20, 2015

Remember, when squaring a negative, it becomes positive. So the min x is -9 and the Max is 9, so the difference is 18

62 Helpful 0 Interesting 2 Brilliant 0 Confused

I forgot the negative value

Evan Huynh - 5 years, 1 month ago

I feel for it too!

Sumant Chopde - 2 years, 4 months ago
Gamal Sultan
Jan 29, 2015

x^2 = 16, 25, 36, 49, 64, 81

Then

x = -4, 4 , -5, 5, -6, 6, -7, 7, -8, 8 , -9, 9

So

maximum x - minimum x = (9) - (-9) = 18

21 Helpful 0 Interesting 0 Brilliant 0 Confused

but sir when we do square of -9, it's 81 but minimum value of x^2 is 9 so how it is possible ?? i think answer should be : maximum value of x is 9 and minimum value of x is -4. ans=9-(-4)= 13

Aryan Omer - 6 years, 4 months ago

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But you just need to find the minimum value of x x , ignore the minimum value of x 2 x^2 . And the minimum value of x x that satisfies the conditions is indeed − 9 -9 .

Rick B - 6 years, 4 months ago

Yes even I accept that the answer is 13

Rushi Bommu - 1 year, 11 months ago
Ahmed Morsy
Jan 29, 2015

x ={ [-9, 3) U (3,9] } max x - min x = 9 -(-9) = 18

6 Helpful 0 Interesting 0 Brilliant 0 Confused

Yes! many people forget about the negative possibilities :)

Chung Kevin - 6 years, 4 months ago
Reduan Rafi
Jan 29, 2015

here the condition is that x is an integer and its squire must grater than 9 and less then 99. if we squire a value above 9 it will break this condition so 9 is the number . and the range of value of x =(-9,-8........-4,4,5,........,8,9) therefore minx=-9 and maxx=9 so, 9-(-9)=18; here the negative value is counted cause if we squire a negative valu it turns into a positive value ..so answer is 18..

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Jakub Smolaga
Oct 29, 2017

Shouldn't the answer be 2√99? (from -√99 to √99)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

the question specified x as an integer so it equals 9

Muhammad Salem - 3 years, 4 months ago

The solution for the inequality 9<x^2<99 is (-sqrt(99),-3) OR (3,sqrt(99)). But x is an integer. So the minimum integral value in the solution is -9 and the maximum integral value in the solution is 9. So the difference between max value & min value is 9-(-9)=18.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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