Question

if a+ 1/a = 0 then show that a^2 - 1/a^2 = 0​

Answer 1

Step-by-step explanation:

a^2 + a + 1 = 0

a^2 + a = -1

a(a + 1) = -1

a + 1 = -1/a

i.e, 1/a = -(a + 1) ... (1)

Now,

a^2 + (1/a)^2

= a^2 + [-(a+1)]^2 ... from eq. (1)

= a^2 + a^2 + 2a + 1

= 2(a^2 + a + 1) - 1

As, a^2 + a + 1 = 0

Thus,

= 2(0) - 1

= 0 - 1

= -1

Thus, the value of a^2 + (1/a)^2 = -1

Answer 2

Answer:

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Step-by-step explanation:

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