Question

if (a^4)+(b^4)=a^2b^2,show that a^6+b^6=0

Answer 1

Hello friend, Here is your answer,

Given, a^(4) + b^(4) = a^(2)b^(2)

To Prove = a^(6) + b^(6) = 0

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
HENCE PROVED