Question

expansion expansion expansion 1 and 3​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

1) 2

2) 322

Step-by-step explanation:

1) If x + 1/x = 2, find x³ + 1/x³

x + 1/x = 2

Cubing on both sides

( x + 1/x )³ = 2³

Using algebraic identity (a + b)³ = a³ + b³ + 3ab(a + b)

x³ + 1/x³ + 3(x)(1/x)( x + 1/x ) = 8

x³ + 1/x³ + 3(2) = 8

x³ + 1/x³ + 6 = 8

x³ + 1/x³ = 8 - 6 = 2

Therefore the value of x³ + 1/x³ is 2.

2) If 3x + 1/3x = 7, find 27x³ + 1/27x³.

3x + 1/3x = 7

Cubing on both sides

( 3x + 1/3x )³ = 7³

Using algebraic identity (a + b)³ = a³ + b³ + 3ab(a + b)

( 3x )³ + ( 1 /3x )³ + ( 3x )( 1/3x )( 3x + 1/3x ) = 343

27x³ + 1/27x³ + 21 = 343

27x³ + 1/27x³ = 343 - 21 = 322

Therefore the value of 3x + 1/3x is 322.