Solution of |x2 - 10| le 6 is

Question

Solution of |x2 - 10| le 6 is (A) (2, 4) (B) (- 4, - 2) (C) (- 4, - 2)∪ (2, 4) (D) [- 4, - 2] ∪ [2, 4]

Tardigrade Admin · Accepted Answer

|x2-10 | le 6 Leftrightarrow - 6 le x 2-10 le 6 Leftrightarrow 4 < x2 le 16 Leftrightarrow 2 le |x| le 4 ∴ either 2 le x le 4 or - 4 le x le - 2 ∴ x∈ [- 4, - 2] ∪ [2, 4]

Q. Solution of $∣ x^{2} - 10∣ \leq 6$ is

$(2, 4)$

$(- 4, - 2)$

$(- 4, - 2) \cup (2, 4)$

$[- 4, - 2] \cup [2, 4]$

$∣ x^{2} - 10∣ \leq 6$
$\Leftrightarrow - 6 \leq x^{2} - 10 \leq 6 \Leftrightarrow 4 < x^{2} \leq 16$
$\Leftrightarrow 2 \leq ∣ x ∣ \leq 4$
$∴$ either $2 \leq x \leq 4$ or $- 4 \leq x \leq - 2$
$∴ x \in [- 4, - 2] \cup [2, 4]$

Q. Solution of ∣x2−10∣≤6 is

(2,4)

(−4,−2)

(−4,−2)∪(2,4)

[−4,−2]∪[2,4]