If (a+1/2)^2=3 then a^3+1/a^3=______
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Answered by
1
Answer:
0
Step-by-step explanation:
( a + 1/a )² = 3
=> a + 1/a = ± √3
Cubing on both sides
=> ( a + 1/a )³ = ( ± √3 )³
Since (a + b)³ = a³ + b³ + 3ab(a + b)
=> a³ + 1/a³ + 3( a )( 1/a )( a + 1/a ) = ± 3√3
=> a³ + 1/a³ + 3( ± √3 ) = ± 3√3
=> a³ + 1/a³ ± 3√3 = ± 3√3
=> a³ + 1/a³ = 0
Answered by
0
Answer:
0
Step-by-step explanation:
(a+1/2)^2=3
a^2 + 1/a^2 + 2 = 3
a^2 + 1/a^2 = 1
a³+1/a³ = (a+1/a)(a²+1/a²-1)
= (a+1/a) (1-1)
= 0
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