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, Problem 77RE
To determine

To find the real solutions of equation xx2+1x+2=8x24 .

Expert Solution

Answer to Problem 77RE

The solution is x=5,2 .

Explanation of Solution

Given information:

  xx2+1x+2=8x24

Formula used:

Properties of fractions:- AC+BC=A+BC .

Distributive property:- a(b+c)=ab+ac

Quadratic Formula:- x=b±b24ac2a .

Calculations:

  =xx2+1(x+2)=8x24

  =x(x+2)(x2)(x+2)+(x2)(x+2)(x2)=8x24 (Re-write in LCD form)

  =x2+2x+x2(x+2)(x2)=8x24=x2+3x2x24=8x24

  =x2+3x2=8 (denominator is same)

  =x2+3x28=0=x2+3x10=0

  a=1b=3c=10

  x=(3)±(3)24(1)(10)2(1)

  x=3±9+402

  x=3±492

  x=3+72=42=2 and x=372=102=5

The solution of the equation x=2,5 .

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