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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q. 45 (page 773)

Solve the system. Use any method you wish.
$\{\begin{cases} \frac{1}{x^{4}} + \frac{6}{y^{4}} = 6 \\ \frac{2}{x^{4}} - \frac{2}{y^{4}} = 19 \end{cases}$

Short Answer

Expert verified

There is no solution to the two equations.

Step by step solution

01

Step 1. Given information.

Consider the given question,

$\{\begin{cases} \frac{1}{x^{4}} + \frac{6}{y^{4}} = 6 . . . . . . (i) \\ \frac{2}{x^{4}} - \frac{2}{y^{4}} = 19 . . . . . . (i i) \end{cases}$

Multiply equation (i) by $x^{4} y^{4}$ ,

$\frac{x^{4} y^{4}}{x^{4}} + \frac{6 x^{4} y^{4}}{y^{4}} = 6 x^{4} y^{4} y^{4} + 6 x^{4} = 6 x^{4} y^{4} . . . . . . (i i i)$

Multiply equation (ii) by $x^{4} y^{4}$ ,

localid="1646932051255" role="math" $\frac{2 x^{4} y^{4}}{x^{4}} - \frac{2 x^{4} y^{4}}{y^{4}} = 19 x^{4} y^{4} 2 y^{4} - 2 x^{4} = 19 x^{4} y^{4} . . . . . . (i v)$

02

Step 2. Multiply equation (iii) by 2.

Multiply equation (iii) by $- 2$ ,

$- 2 y^{4} - 12 x^{4} = - 12 x^{4} y^{4} . . . . . . (v)$

Add equations (v) and (iv),

$(2 y^{4} - 2 x^{4}) + (- 2 y^{4} - 12 x^{4}) = 19 x^{4} y^{4} - 12 x^{4} y^{4} - 14 x^{4} = 7 x^{4} y^{4} y^{4} = - \frac{1}{2}$

Taking square root of the two sides isn't possible.

Hence, there is no solution.

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