Question

if sum of a/b and it's reciprocal is 1 and a≠0,b≠0 then, find the value of a³+b³=?

Answer 1

the answer is 0 and the process is above

Answer 2

The value of a³ + b³ = 0

Given:

The sum of a/b and its reciprocal is 1  

Where a ≠ 0 and b ≠ 0  

To find:

The value of a³+b³  

Solution:

Formula used:

From algebraic identities

a³ + b³ = (a + b)(a² - ab + b²)  

From the data,

The sum of a/b and its reciprocal is 1

Here reciprocal of a/b is b/a

=> a/b + b/a = 1

=> (a² + b²)/ab = 1   [ take ab as LCM ]

=> (a² + b²) = ab  

=> a² + b² - ab = 0 --- (1)

From algebraic identities,

=> a³ + b³ = (a + b)(a² - ab + b²)  

=> a³ + b³ = (a + b)(0)  

=> a³ + b³ = 0      [ ∵ Anything multiplied by zero is 0 ]

Therefore,

The value of a³ + b³ = 0  

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