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Solve this plss ?
if (a + 1/a )^2 = b
then what is (a^3 + 1/a^3) in terms of b ?
4 Answers
- 7 years agoFavorite Answer
note that ( x^3 + y^3 ) = (x+y) ( x^2 - xy + y^2)
(a^3 + 1/a^3 ) = ( a + 1/a) ( a^2 - a/a + 1/a^2)
(a^3 + 1/a^3 ) = ( a+1/a) ( a^2 + 1/a^2 -1) .....(i)
now, (a+1/a) ^2 = b
= a^2 + 2a/a + 1/a^2 =b
= a^2 + 1/a^2 = b-2 .....(ii)
and , (a+1/a) = +/- sqrt(b) ....(iii)
put (ii) and(iii) in (i),
(a^3 + 1/a^3) = +/- sqrt(b) ( b-2-1)
= +/- sqrt(b) (b-3) .....ans
- EliotLv 57 years ago
If you expand (a + 1/a)³ you will get...
aâ + â a³ + 3(a + 1/a)
therefore aâ + â a³ = 3âb + âb³
- 7 years ago
[a + ( 1 / a ) ]^3 = a^3 + 3a + (3 / a ) + 1 / a^3
b^( 3 / 2 ) = a^3 + (1 / a^3 ) + 3 sqrt ( b )
b^( 3 / 2 ) - 3 sqrt b = a^3 + ( 1 / a^3 )
Source(s): my brain
