Question

4. If a-b =5,and ab =12,find a²+b² and a³-b³
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Answer 1

Answer:

a² + b² = 49

a³ - b³ = 305

Step-by-step explanation:

Given that,

(a - b) = 5

ab = 16

Required to find,

a² + b²

a³ - b³

We know that,

 a² + b²

=(a - b)² + 2ab                                  

=(5²) + 2.12                                  [As a - b = 5 and ab = 12]

= 25 + 24

= 49

So a² + b² = 49

 a³ - b³

=(a - b)(a² + ab + b²)                  [As (a - b) = 5 ]

=5(a² + b² + ab)                        

=5(49 + 12)                                [As ab = 12 and a² + b² = 49]

=5(61)

=305

So a³ - b³ = 305