Question

I don't know how to solve and I have to show my work on the questions please help

Answer 1

The value of y is 81.

Explanation:

See the steps below :

`√(y) - \sqrt[4]{y} - 6 = 0`

`{y}^{ (1)/(2) } - {y}^{ (1)/(4) } - 6 = 0`

`let \: {y}^{ (1)/(4) } = x`

`{x}^(2) - x - 6 = 0`

`(x + 2)(x - 3) = 0`

`x = - 2`

`{y}^{ (1)/(4) } = - 2`

`log( {y}^{ (1)/(4) } ) = log( - 2) \: (rejected)`

`x = 3`

`{y}^{ (1)/(4) } = 3`

`log( {y}^{ (1)/(4) } ) = log(3)`

`(1)/(4) log(y) = log(3)`

`log(y) = 4 log(3)`

`log(y) = log( {3}^(4) )`

`log(y) = log(81)`

`y = 81`

Answer 2

√y - ⁴√y - 6 = 0

(⁴√y)² - ⁴√y - 6 = 0

u² - u - 6 = 0

u = 3 and u = -2

⁴√y = 3

y = 81

⁴√y = -2

y ∈ R

Answer: y = 81

Best of Luck!