if a cube + b cube =9 and a + b =3 then the value of 1/a +1/b
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GIVEN :
a³ + b³ = 9
a + b = 3
TO FIND :
Value of 1/a + 1/b
SOLUTION :
a³ + b³ = 9 -----(1)
a + b = 3 ----(2)
We know that,
a³ + b³ = (a + b)³ - 3ab (a + b)
9 = (3)³ - 3ab(3)
9 = 27 - 9ab
9ab = 27 - 9
9ab = 18
ab = 18/9
ab = 2
Now,
1/a + 1/b
= b + a /ab
= a + b /ab
= 3/2
Therefore, the value of 1/a + 1/b = 3/2.
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