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if a^4+b^4=a^2b^2

show that a^6+b^6=0
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8 months ago

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

8 months ago
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