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Mathematics

Assertion (A): If a2 - 8a - 1 = 0.

⇒ a2a−8aa−1a=0\dfrac{a^2}{a} - \dfrac{8a}{a} - \dfrac{1}{a} = 0

⇒ a−1aa-\dfrac{1}{a} = 8 is not true.

Reason (R): The division of each term of the equation a2 - 8a - 1 = 0 is defined only when a is not equal to 0 (zero).

  1. A is true, R is false.
  2. A is false, R is true.
  3. Both A and R are true.
  4. Both A and R are false.

Expansions

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Answer

Both A and R are false.

Explanation

Given,

a2 - 8a - 1 = 0

Dividing each term by a,

⇒a2a−8aa−1a=0a⇒a−8−1a=0⇒(a−1a)−8=0⇒(a−1a)=8⇒ \dfrac{a^2}{a} - \dfrac{8a}{a} - \dfrac{1}{a} = \dfrac{0}{a}\\[1em] ⇒ a - 8 - \dfrac{1}{a} = 0\\[1em] ⇒ (a - \dfrac{1}{a}) - 8 = 0\\[1em] ⇒ (a - \dfrac{1}{a})= 8\\[1em]

∴ Assertion (A) is false.

a2 - 8a - 1 = 0

⇒ a(a - 8) - 1 = 0

⇒ a(a - 8) = 1

⇒ a = 1(a−8)\dfrac{1}{(a - 8)}

∴ Reason (R) is false.

Hence, both Assertion (A) and Reason (R) are false.

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