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Mathematics

Statement 1: (x0 + y0)(x + y)0 = 1, x, y ≠ 0.

Statement 2: (1 + 1)(1 - 1) = 2 x 0 = 0.

Which of the following options is correct?

  1. Both the statements are true.

  2. Both the statements are false.

  3. Statement 1 is true, and statement 2 is false.

  4. Statement 1 is false, and statement 2 is true.

Exponents

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Answer

We know that,

For any number a ≠ 0, a0 = 1.

a0 = 1

Statement 1 : (x0 + y0)(x + y)0 = 1

Solving L.H.S. of the above equation :

⇒ (1 + 1) x 1

⇒ 2 x 1

⇒ 2.

R.H.S. = 1

Since, L.H.S. ≠ R.H.S.

So, statement 1 is false.

Statement 2 : (1 + 1)(1 - 1) = 2 x 0 = 0

Solving L.H.S. of the above equation :

⇒ (1 + 1)(1 - 1)

⇒ 2 x 0

⇒ 0.

R.H.S. = 0

Since, L.H.S. = R.H.S.

So, statement 2 is true.

Hence, option 4 is the correct option.

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