Question

If a2-2a-1=0,then a2+1/a2=

Answer 1

Answer:

we get answer as 6

Step-by-step explanation:

a2 - 2a - 1 = 0

a(a - 2) = 1

a - 2 = 1/a

a - 1/a = 2 ---- i)

a2 + 1/a2

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

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

taking here a = a and b = -(1/a)

(a + (- 1/a))2 - 2 (a) (- 1/a)

(a - 1/a)2 + 2

putting the value of a - 1/a = 2 from (i)

(2)2 + 2 = 4+2 = 6

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Answer 2

Answer:

a^2+1/a^2 = 6

Step-by-step explanation:

a^2 - 2a - 1 = 0

a(a-2) - 1 = 0

a(a-2) = 1

a-2 = 1/a

a = 1/a + 2

a-1/a = 2

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

a^2 + 1/a^2 - 2 = 4

a^2 + 1/a^2 = 6