Question

a^4+b^4=a^2*b^2
then find the value of:

a^6+b^6​

Answer 1

Answer:

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Step-by-step explanation:

Given:-

    a^(4) + b^(4) = a^(2) b^(2)

To Find:-

    a^(6) + b^(6) = 0

Solution:-

   We can write a^(6) + b^(6) as (a^(2))^(3) + (b^(2))^(3)

   So, we got the formula of x^(3) + y^(3)

  where x = a^2 and y = b^(2)

   Now open the formula =

  x^3 + y^3 = (x + y) (x^2 + y^2 - xy)

   Now, put the values of x and y,

  a^6 + b^6 = (a^2 + b^2) (a^4 + b^4 - a^2b^2)

   and given, a^4 + b^4=a^2b^2

   So,

  a^6+b^6 = (a^2 + b^2) (a^2b^2 - a^2b^2)

   therefore,

  a^6 + b^6 = 0

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