Question

The number of ordered pairs (a, b), (where a, b ∈ R) satisfying the equation a²⁰⁰⁸ + b²⁰⁰⁸ = 2008 |a||b| – 2006 is equal to ______.

Options

• 2.00

• 3.00

• 4.00

• 5.00

Answer 1

The number of ordered pairs (a, b), (where a, b ∈ R) satisfying the equation a²⁰⁰⁸ + b²⁰⁰⁸ = 2008 |a||b| – 2006 is equal to 4.00.

Explanation:

`(a^2008 + b^2008 + 2006)/2008 ≥ (a^2008.b^2008 xx 1)^(1/2008)`

a²⁰⁰⁸ + b²⁰⁰⁸ + 2006 > 2008 |a||b|

∴ a²⁰⁰⁸ + b²⁰⁰⁸ + 2006 = 2008|a||b|

If a²⁰⁰⁸ = b²⁰⁰⁸ = 1

a = 1, –1 and b = 1, –1

 Total solutions are 4.