Chapter 11.6, Problem 61AYU

In Problems 57-64, use a graphing utility to solve each system of equations.Express the solution(s) rounded to two decimal places.

$\{\begin{array}{l}{x}^4\text{ + }{y}^4\text{ = 1}2\\ x{y}^2\text{ = }2\end{array}$

To determine

To solve: The system of equations by using graphical utility.

Answer to Problem 61AYU

Solution:

$x = 0.58,y = 1.86$ or $x = 0.58,y = - 1.86$ or $x = 1.81,y = 1.05$ or $x = 1.81,y = - 1.05$

Explanation of Solution

Given:

$x^4 + y^4 = 12$    -----(Eq 1)

$x{y}^2 = 2$    -----(Eq 2)

Graph:

It can be seen from the graph that the curves for the equations intersect at $(0.58,1.86)$, $(0.58,\text{-}1.86)$, $(1.81,1.05)$ and $(1.81,\text{-}1.05)$.

Hence the solution to the given system of equations is $(0.58,1.86)$, $(0.58,\text{-}1.86)$, $(1.81,1.05)$ and $(1.81,\text{-}1.05)$.