Question

A-1/a=2/3 for some real number a. Find a^4+1/a^4

Answer 1

`1 (1)/(81) \`

Solution:

`(a - 1)/(a) = (2)/(3)`

1) 2a = 3(a - 1)

2a = 3a - 3

2a - 3a = -3

-a = -3 / * (-1)

a = 3

2) Replace the a with 3 in this:

`\frac{ {a}^(4) + 1}{ {a}^(4) }`

`\frac{ {3}^(4) + 1}{ {3}^(4) } = (81 + 1)/(81) = (82)/(81) = 1 (1)/(81)`

I don't know if I got this right, but at least I tried