Question

which integral values of a satisfy the equation of a to the power 100=1?​

Answer 1

Given :      a¹⁰⁰  = 1

To Find :   which integral values of a satisfy the equation

Solution :

a¹⁰⁰  = 1  

=> (a²)⁵⁰ = 1

=> a² = 1

=> a² - 1 = 0

=> (a + 1)(a - 1) = 0

a + 1 = 0 => a = - 1

a - 1 = 0 => a = 1

a = 1 , - 1  satisfy the equation a¹⁰⁰  = 1

1¹⁰⁰  = 1

(-1)¹⁰⁰ = 1

a = 1 , - 1  satisfy the equation  a¹⁰⁰  = 1

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