Question

.If x^3+3/x=4*(a^3+b^3);
3x+1/x^3=4(a^3-b^3)​

Answer 1

Answer:

x = a + b and 1 / x = a - b

Step-by-step explanation:

Given --->

x³ + 3 / x = 4 ( a³ + b³ )

3 x + 1 / x³ = 4 ( a³ - b³ )

To find ---> Value of x and 1/x .

Solution--->

(1) Plzz see the attachement

(2) Now initially we add given equation and apply an identity which is as follows

( a + b )³ = a³ + b³ + 3a b ( a + b )

Using it and taking cube root of both sides we get a new equation as

x + 1/x = 2a ............ ( 3 )

(3) Now we subtract given equation and apply following identity

( a - b )³ = a³ - b³ - 3 ab ( a - b )

Using it and taking cube root of both sides we get a new equation as

x - 1 / x = 2b ................ ( 4 )

(4 ) Now solving equation (3 ) and ( 4 ) we get

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