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Mathematics

If a - b = 1 and a + b = 3, the value of ab is:

  1. 4

  2. 2

  3. -2

  4. 0

Identities

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Answer

Using the formula,

[∵(x + y)2 = x2 + 2xy + y2]

And

[∵(x - y)2 = x2 - 2xy + y2]

(a + b)2 = a2 + 2ab + b2

Putting a + b = 3, we get

(3)2 = a2 + 2ab + b2

9 = a2 + 2ab + b2

9 - 2ab = a2 + b2 ……………(1)

And,

(a - b)2 = a2 - 2ab + b2

Putting the value, a - b = 1

(1)2 = a2 - 2ab + b2

1 = a2 + b2 - 2ab

Using equation (1)

1 = 9 - 2ab - 2ab

1 = 9 - 4ab

4ab = 9 - 1

4ab = 8

ab = 84\dfrac{8}{4}

ab = 2

Hence, option 2 is the correct option.

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