Let A = { x : | x 2 - 10 | 6 } and B = { x : | x - 2 | 1 } . Then [2026]

Question

Let $A = {x : | x^{2} - 10 | \leq 6} and B = {x : | x - 2 | > 1} .$ Then [2026]

Smart Achievers · Accepted Answer

(4)

$| x^{2} - 10 |$ $\leq 6$

$- 6 \leq x^{2} - 10 \leq 6$

$4 \leq x^{2} \leq 16$

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

$| x - 2 |$ $> 1$

$B = (- \infty, 1) \cup (3, \infty)$

$A \cup B = (- \infty, 1) \cup [2, \infty)$

$A \cap B = [- 4, - 2] \cup (3, 4]$

$A - B = [2, 3]$

$B - A = (- \infty, - 4) \cup (- 2, 1) \cup (4, \infty)$

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