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Chapter 11: Q. 61 (page 773)

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

role="math" localid="1646902405632" x4+y4=12xy2=2

Short Answer

Expert verified

The graph of the system of equationsx4+y4=12xy2=2 is,

From the graph, the solutions of the given system are, role="math" localid="1646902921738" 1.81,1.05,1.81,-1.05,0.58,1.56,0.58,-1.56.

Step by step solution

01

Step 1. Given information

x4+y4=12xy2=2

First we need to solve the given equations for y.

x4+y4=12y4=12-x4lny4=ln12-x44lny=ln12-x4lny=ln12-x44y=eln12-x44

Next solve the second equation.

xy2=2y2=2xy=卤2x

02

Step 2 Now sketch a graph for the obtained equations.

In the graph, the two equations are intersecting at four points. They are, 1.81,1.05,1.81,-1.05,0.58,1.56,0.58,-1.56.

So, the system has four solutions.

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