Chapter 11.6, Problem 45AYU

To determine

To solve: The given system of equation.

Answer to Problem 45AYU

Solution:

No real solution exists.

Explanation of Solution

Given:

$\frac{1}{x^4} + \frac{6}{y^4} = 6$   -----(Eq 1)

$\frac{2}{x^4} - \frac{2}{y^4} = 19$   -----(Eq 2)

Calculation:

Substituting $\frac{1}{x^4} = 6 - \frac{6}{y^4}$ in Eq 2 we get

$12 - \frac{12}{y^4} - \frac{2}{y^4} = 19$

The above equation can be rewritten as

$-7y^4 - 14 = 0$

$y^4 = -2$

$y^2 = \pm \sqrt{2}i$

Therefore, no real solution exist.