Question

if 6x/(2x^2+5x-2)=1,x>0,then find value of x^3+1/x^3​

Answer 1

Given : 6x/(2x²+5x-2)=1, x>0

To find :   x^3+  1/x^3​     x³  + 1/x³

Step-by-step explanation:

6x/(2x² + 5x  - 2)  = 1

=> 2x² + 5x  - 2 = 6x

=>  2x² -  x  - 2 =  0

=> x  = (1  ± √1 + 16) / (2* 2)

=> x  = ( 1 ±  √17)/4

x>0

=>  x = ( √17 + 1 )/4

1/x = 4/(√17 + 1  )  = 4(√17 - 1) / ( 17 - 1)  = (√17 - 1 )/4

x = ( √17 + 1 )/4  , 1/x  =  (√17 - 1 )/4

x + 1/x  =  2√17/4 = √17 / 2

x³  + 1/x³  = (x + 1/x)³  -3x(1/x)(x + 1/x)

= (√17 / 2 )³  - 3(√17 / 2)

= 17√17  / 8 -  12√17  / 8

= 5√17  / 8

x³  + 1/x³  =    5√17  / 8

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