Let S = { x [ - 6 , 3 ] - { - 2 , 2 } : | x + 3 | - 1 | x | - 2 0 } and T = { x Z : x 2 - 7 | x | + 9 0 } . Then the number of elements in S T is

Question

Let $S = {x \in [- 6, 3] - {- 2, 2} : \frac{| x + 3 | - 1}{| x | - 2} \geq 0}$ and $T = {x \in Z : x^{2} - 7 | x | + 9 \leq 0} .$ Then the number of elements in $S \cap T$ is

Smart Achievers · Accepted Answer

(4)

$- 6 \leq x \leq - 4, x = 3 & | x | \leq \frac{7 + \sqrt{13}}{2} \Rightarrow x = - 5, - 4, 3$

Solution

Q.
Let $S = {x \in [- 6, 3] - {- 2, 2} : \frac{| x + 3 | - 1}{| x | - 2} \geq 0}$ and $T = {x \in Z : x^{2} - 7 | x | + 9 \leq 0} .$ Then the number of elements in $S \cap T$ is

1 7

2 5

3 4

4 3

Ans.
(4)

$- 6 \leq x \leq - 4, x = 3 & | x | \leq \frac{7 + \sqrt{13}}{2} \Rightarrow x = - 5, - 4, 3$

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Solution

Q. Let S={x∈[-6,3]-{-2,2}:|x+3|-1|x|-2≥0} and T={x∈Z:x2-7|x|+9≤0}. Then the number of elements in S∩T is

1 7

2 5

3 4

4 3

Ans. (4) -6≤x≤-4, x=3 & |x|≤7+132⇒x=-5,-4,3

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Q.
Let $S = {x \in [- 6, 3] - {- 2, 2} : \frac{| x + 3 | - 1}{| x | - 2} \geq 0}$ and $T = {x \in Z : x^{2} - 7 | x | + 9 \leq 0} .$ Then the number of elements in $S \cap T$ is

Ans.
(4)

$- 6 \leq x \leq - 4, x = 3 & | x | \leq \frac{7 + \sqrt{13}}{2} \Rightarrow x = - 5, - 4, 3$