Question

If x3+3/x=4(a3+b3) and 3x+3/x3=4(a3-b3) then prove that , (a2- b2)=1

Answer 1

a² - b² = 1  if  x³ + 3/x  = 4 (a³ + b³) & 3x + 1/x³  = 4(a³ - b³)

Step-by-step explanation:

Correct Question is : if  x³ + 3/x  = 4 (a³ + b³) & 3x + 1/x³  = 4(a³ - b³)

then a² - b²

x³ + 3/x  = 4 (a³ + b³)    Eq1

3x + 1/x³  = 4(a³ - b³)    Eq2

Adding both  (eq1 + eq2)

x³ + 1/x³   + 3(x + 1/x)  =  8a³

=> (x + 1/x)³  = 8a³

=> x + 1x = 2a     -eq3

on subtraction (eq 1 - Eq2)

x³ - 1/x³   - 3(x - 1/x)  =  8b³

=> (x  - 1/x)³ = (2b)³

=> x - 1/x  = 2b     Eq4

Adding both  (eq 3 + eq4)

2x = 2a + 2b

=> x = a + b     Eq5

on subtracting  (eq3 - eq 4)

2/x = 2a - 2b

=> 1/x = a - b    Eq6

on multiplying  (eq5 * eq 6)

x(1/x) = (a + b)(a - b)

=> 1 = a² - b²

=>  a² - b² = 1

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