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Mathematics

If a+1a=2.5 and a−1a=1.5a + \dfrac{1}{a} = 2.5 \text{ and } a - \dfrac{1}{a} = 1.5, the value of (a+1a)2−(a−1a)2\Big(a + \dfrac{1}{a}\Big)^2 - \Big(a - \dfrac{1}{a}\Big)^2 is :

  1. 4

  2. 2

  3. 1

  4. 8.5

Expansions

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Answer

Solving,

⇒(a+1a)2−(a−1a)2⇒(2.5)2−(1.5)2⇒6.25−2.25⇒4.\Rightarrow \Big(a + \dfrac{1}{a}\Big)^2 - \Big(a - \dfrac{1}{a}\Big)^2 \\[1em] \Rightarrow (2.5)^2 - (1.5)^2 \\[1em] \Rightarrow 6.25 - 2.25 \\[1em] \Rightarrow 4.

Hence, Option 1 is the correct option.

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