Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…

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Question

Chapter 5.6, Problem 40WE

To determine

To find the value of constants A and B in the given equation.

Expert Solution & Answer

Answer to Problem 40WE

A=3 and B=−1

Explanation of Solution

Given:

Equation: 2x+9x2−x−6=Ax−3+Bx+2

Calculation:

Consider Left Hand Side,

⇒2x+9x2−x−6

Factoring the denominators,

⇒2x+9(x−3)(x+2)

Now, solving the above equation,

2x+9(x−3)(x+2)=Ax−3+Bx+2

=A⋅(x+2)(x−3)⋅(x+2)+B⋅(x−3)(x+2)⋅(x−3)

=Ax+2A(x−3)(x+2)+Bx−3B(x−3)(x+2)

=Ax+2A+Bx−3B(x−3)(x+2)=Ax+Bx+2A−3B(x−3)(x+2)

2x+9(x−3)(x+2)=x(A+B)+(2A−3B)(x−3)(x+2)

2x+9=x(A+B)+(2A−3B)

Comparing Left Hand Side and Right Hand Side,

2=A+B.......(i)9=2A−3B.......(ii)

Multiplying equation (i) by 3 ,

3A+3B=6.......(iii)

Adding equations (ii) and (iii),

⇒(3A+3B)+(2A−3B)=6+9⇒3A+3B+2A−3B=15⇒5A=15⇒A=3

Substituting the value of A in equation (iii),

⇒3×3+3B=6⇒9+3B=6⇒3B=6−9⇒3B=−3⇒B=−1

Conclusion:

Therefore, the value of A=3 and B=−1 .

Chapter 5.6, Problem 39WE

Chapter 5.6, Problem 41WE

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

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