Question

If, x²+ 1 /25x² is equal to 43/5, find x³ + 1 /125x³. (Expansions) Please help !!

Answer 1

Answer:

Step-by-step explanation:

Given ,

x² + 1/25x² = 43/5

( x + 1/5x )² = x² + 1/25x² + 2/5

( x + 1/5x )² = 43/5 + 2/5

( x + 1/5x )² = (43 + 2)/5

( x + 1/5x )² = 45/5

( x + 1/5x )² = 9

x + 1/5x = √9

x + 1/5x = 3 or - 3[Since, 3² = 9 and (-3)² = 9 too]

When, x + 1/5x = 3,

( x + 1/5x )³ = ( 3 )³

x³ + 1/125x³ + 3/5( x + 1/5x ) = 27

x³ + 1/125x³ + (3/5) * 3 = 27

x³ + 1/125x³ = 27 - 9/5

x³ + 1/125x³ = ( 135 - 9 )/5

x³ + 1/125x³ = 126/5 = 25.2

When, x + 1/5x = - 3,

( x + 1/5x )³ = ( - 3 )³

x³ + 1/125x³ + 3/5( x + 1/5x ) = - 27

x³ + 1/125x³ + 3/5( - 3 ) = - 27

x³ + 1/125x³ = - 27 + 9/5

x³ + 1/125x³ = - 126/5 = - 25.2

Therefore ,

x³ + 1/125x³ = 25.2 or - 25.2

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