find the value of a³+1/a³ if a²+1/a²=1
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Answered by
1
since
a²+1/a²=1,
then
(a+1/a)²=a²+1/a²+2,
(a+1/a)²=1+2=3,
then
(a+1/a)=√3,
therefore
a³+1/a³=(a+1/a)(a²+1/a²-1),
a³+1/a³=√3×(1-1),
then
a³+1/a³=√3×0=0
a²+1/a²=1,
then
(a+1/a)²=a²+1/a²+2,
(a+1/a)²=1+2=3,
then
(a+1/a)=√3,
therefore
a³+1/a³=(a+1/a)(a²+1/a²-1),
a³+1/a³=√3×(1-1),
then
a³+1/a³=√3×0=0
Answered by
1
Answer:
a3+1/a3=0
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