Question : If $a^{4} + b^{4} = a^{2}b^{2}$, then $(a^{6} + b^{6})$ equals:
Option 1: $0$
Option 2: $1$
Option 3: $a^{2}+b^{2}$
Option 4: $a^{2}b^{4}+a^{4}b^{2}$
Answer (1)
15th Jan, 2024
Correct Answer: $0$
Solution :
Given: $a^{4} + b^{4} = a^{2}b^{2}$
Now, $(a^{6} + b^{6})$
$=(a^2)^3+(b^2)^3$
$=(a^{2} + b^{2})(a^{4} + b^{4} - a^{2}b^{2})$
$= (a^{2} + b^{2})(a^{2}b^{2} - a^{2}b^{2})$
$=0$
Hence, the correct answer is $0$.
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