If 2a + 2/a = 4, what is the value of 2a^2 - 2/a^2?

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Step-by-step explanation:

2a + 2/a = 4

Multiply each side by a to clear the fraction

a (2a + 2/a) = 4*a

Distribute

2a^2 + 2 = 4a

Subtract 4a from each side

2a^2 - 4a + 2 = 4a-4a

2a^2 - 4a + 2 = 0

Divide by 2

2/2 a^2 - 4a/2 + 2/2 = 0/2

a^2 - 2a + 1=0

Factor

(a-1) (a-1) = 0

Using the zero product property

a=1

2a^2 - 2/a^2

2 (1) ^2 - 2/1^2

2-2

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