Question

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

Answer 1

Answer:

The value of y is 81.

Step-by-step explanation:

See the steps below :

$\sqrt{y} - \sqrt[4]{y} - 6 = 0$

${y}^{ \frac{1}{2} } - {y}^{ \frac{1}{4} } - 6 = 0$

$let \: {y}^{ \frac{1}{4} } = x$

${x}^{2} - x - 6 = 0$

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

$x = - 2$

${y}^{ \frac{1}{4} } = - 2$

$log( {y}^{ \frac{1}{4} } ) = log( - 2) \: (rejected)$

$x = 3$

${y}^{ \frac{1}{4} } = 3$

$log( {y}^{ \frac{1}{4} } ) = log(3)$

$\frac{1}{4} log(y) = log(3)$

$log(y) = 4 log(3)$

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

$log(y) = log(81)$

$y = 81$

Answer 2

Solution:

√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!