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# How many integrals value of x satisfy the inequality

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Manager
Joined: 10 Apr 2018
Posts: 179
How many integrals value of x satisfy the inequality  [#permalink]

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25 Sep 2018, 20:13
1
00:00

Difficulty:

65% (hard)

Question Stats:

46% (02:11) correct 54% (01:18) wrong based on 28 sessions

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How many integrals value of x satisfy the inequality $$(1-x^2)(4-x^2)(9-x^2) > 0 ?$$

(A)0

(B)1

(C)3

(D)5

(E)Greater than 5
Manager
Joined: 11 Mar 2018
Posts: 90
Re: How many integrals value of x satisfy the inequality  [#permalink]

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25 Sep 2018, 20:33
Probus wrote:
How many integrals value of x satisfy the inequality $$(1-x^2)(4-x^2)(9-x^2) > 0 ?$$

(A)0

(B)1

(C)3

(D)5

(E)Greater than 5

As we have to consider only integral values, we start as,

For x=0
On substituting,
(1-0)(4-0)(9-0) >0

Hence true for x = 0

For x = 1 or -1 (As x is squared we can consider both negative and positive values of the number)
On substituting,
(1-1)(4-1)(9-1) =0

Hence not true for x = 1 or -1

For x = 2 or -2
On substituting,
(1-4)(4-4)(9-4) =0

Hence not true for x = 2 or -2

For x = 3 or -3
On substituting,
(1-9)(4-9)(9-9) =0

Hence not true for x = 3 or -3

For x = 4 or greater than 4 OR -4 or lesser than -4
On substituting,
(1-16)(4-16)(9-16) < 0

Hence not true for x = 4 or greater than 4 OR -4 or lesser than -4

Hence only one value satisfies that is x = 0

_________________

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Intern
Joined: 08 Aug 2018
Posts: 6
Re: How many integrals value of x satisfy the inequality  [#permalink]

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25 Sep 2018, 23:14
So when $$x^2$$ = 1, 4 or 9 the equation equals to 0.
Which implies equation is 0, when x = -3, -2, -1, 1, 2 or 3.

Note: for the equation to be greater than 0, we need all three parts ($$(1−x^2)$$, $$(4−x^2)$$ & $$(9−x^2)$$) of the equation to either be positive or exactly 2 to be negative and 1 positive.

Only 3 situations to consider here -
(1) When substituting x < -3, the equation does not hold true as it results in a negative value.
(2) When substituting x > 3, the equation does not hold true as it results in a negative value
(3) Only possible value left is 0 and this fits the equation nicely.

So only 1 value (x=0) satisfies the given inequality.

Ans: B
Re: How many integrals value of x satisfy the inequality &nbs [#permalink] 25 Sep 2018, 23:14
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