Mathematics
Assertion (A) : If x is a real number then (x - 2)2 > 4 ⇒ x > 4.
Reason (R) : x2 > 4 ⇒ 2 < x < -2.
A is true, R is false.
A is false, R is true.
Both A and R are true.
Both A and R are false.
Linear Inequations
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Answer
Solving,
⇒ (x - 2)2 > 4
⇒ x2 + 4 - 4x > 4
⇒ x2 - 4x + 4 - 4 > 0
⇒ x2 - 4x > 0
⇒ x(x - 4) > 0
1st case :
⇒ x > 0 and x - 4 > 0
⇒ x > 0 and x > 4
⇒ x > 4.
2nd case :
⇒ x < 0 and x - 4 < 0
⇒ x < 0 and x < 4
⇒ x < 0.
Solution set = {x < 0 or x > 4}.
∴ Assertion (A) is false.
Solving,
⇒ x2 > 4
⇒ x2 - 4 > 0
⇒ x2 - 22 > 0
⇒ (x + 2)(x - 2) > 0
1st case :
⇒ (x + 2) > 0 and (x - 2) > 0
⇒ x > -2 and x > 2
⇒ x > 2 ………..(1)
2nd case :
⇒ (x + 2) < 0 and (x - 2) < 0
⇒ x < -2 and x < 2
⇒ x < -2 ……….(2)
From equation (1) and (2), we get :
⇒ 2 < x < -2.
∴ Reason (R) is true.
Hence, Option 2 is the correct option.
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