BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.9, Problem 31E
To determine

To calculate: The value of x from the equation x4=5x+12 by algebraic method and graphical method.

Expert Solution

Answer to Problem 31E

The value of x is 4 and Graph of the equation is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 31E , additional homework tip  1

Explanation of Solution

Given information:

The equation x4=5x+12 .

Calculation:

It is provided that the equation x4=5x+12 .

Algebraic method;

The method in which isolate x on one side of the equation and solve the value of x .

Subtract x from the equation x4=5x+12 ,

  x+x4=5xx+124=4x+12

Subtract -12 from the equation,

  412=4x+121216=4x4=x

Therefore, the value of x=4 .

Graphical method;

Let put y1=x4 and y2=5x+12

The graph of the equation y1=x4 can be sketched using the table,

    xy
    04
    22
    40
    27
    48

The graph of equation is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 31E , additional homework tip  2

The graph of the equation y2=5x+12 can be sketched using the table,

    xy
    012
    222
    432
    22
    48

The graph of equation is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 31E , additional homework tip  3

The graph of both equations in same figure is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 31E , additional homework tip  4

The solution is the x coordinate of the intersection point (4,8)  of the two graphs. So, the intersection point on the x coordinate is 4 .

Thus, the value of x is 4

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