Question
a^4/4 +4/a^4 +1factorise..+1 is not included 4a^4
Answers
Reiny
so we have (a^4/4) + (4/a^4) + 1
= (a^8 + 16 + 4a^4)/(4a^4)
= a^8 <b>+ 8a^4</b> + 16 + 4a^4 <b>- 8a^4</b>)/(4a^4) <---- completing the square
= ( (a^4 + 4)^2 - 4a^4)/(4a^4)
= (a^4 + 4 + 2a^2)(a^4 + 4 - 2a^2)/(4a^4)
= (a^8 + 16 + 4a^4)/(4a^4)
= a^8 <b>+ 8a^4</b> + 16 + 4a^4 <b>- 8a^4</b>)/(4a^4) <---- completing the square
= ( (a^4 + 4)^2 - 4a^4)/(4a^4)
= (a^4 + 4 + 2a^2)(a^4 + 4 - 2a^2)/(4a^4)