Question

If (a+1/2)=4find the value of a^3+1/a^3​

Answer 1

Explanation:

`a + (1)/(2)=4\\\\`

`a = 4 -(1)/(2)\\\\a =(4*2)/(1*2)-(1)/(2)\\\\a =(8)/(2)-(1)/(2)\\\\a=(7)/(2)`

`(1)/(a)=(1)/((7)/(2))\\\\ = 1*(2)/(7)\\\\ = (2)/(7)`

`a^(3)+(1)/(a^(3))=((7)/(2))^(3)+((2)/(7))^(3)`

`= (343)/(8)+(8)/(343)\\\\=(343*343)/(8*343)+(8*8)/(343*8)\\\\=(117649)/(2744)+(64)/(2744)\\\\=(117649+64)/(2744)\\\\=(117713)/(2744)\\\\= 42(2465)/(2744)`