Latest Elitmus Aptitude Question SOLUTION: [(2X+9)^2]/(X+3) is an integer for how many values of X?

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(#M40157163) ELITMUS Numerical Ability question Number System Keep an EYE

[(2X+9)^2]/(X+3) is an integer for how many values of X?

Asked In Elitmus Shubhi Sharma (7 years ago)

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rahul gupta  (7 years ago)

values are -2,-4,0,-6,6,-12

Is this solution Helpfull? Yes (16) | No (3)  

swati  (7 years ago)

[(2x+9)^2]=4x^2+36x+81 when div by x+3 leaves (4x+24) as quotient and 9 as remainder .
so, the above question can be writen as (4x+24)+[9/(x+3)]. so this can be integer only for 0,-2,-4,-6,6,-12

Is this solution Helpfull? Yes (8) | No   

shailendra  (7 years ago)

Above expression can be simplified as 2 + (3 / ( x+3))
thereby checking the values suitable for getting integer in above expression, we get
X={0, -2, -4,- 6}

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Manikanta  (7 years ago)

for two values..o and -2

Is this solution Helpfull? Yes (1) | No (6)  

Amit Kumar Singh  (7 years ago)

when putting positive values = 1,2,3,4,5 the corresponding values will like
Numerator= 11, 13, 15 , 17, 19.....
Denominator= 4, 5, 6, 7, 8.... the N= 2D+3 so there will be no integer when value of x will positive

when values is negative -2,-4 and 0 it will result integer =5,-1 and 3

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Shahanaa  (7 years ago)

(2X=9)^2 / X+3 , INTEGER VALUES APPLY ARE -2,-1,0

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Suraj Kesharwani  (6 years ago)

The above equation can be break in form like [(2x + 6) + 3]^2 / (x + 3) so it will be broken
after applying formulae for (a+b)^2 taking (2x + 6) as 'a' and 3 as 'b' we get,
= 4(x+3) + 36 / (x+3) + 12
for this the value of x which satisfy are (-2, -1, 0, 1, 3, 6, 9, 15)

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