   Chapter A.5, Problem 39E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 37-39, c 2 = a 2 + b 2 .In the right triangle, find a if b = a + 3     a n d     c = a + 4 . To determine

To find:

To find a if b=a+3andc=a+4.

Explanation

Consider the following equation,

c2=a2+b2.

The diagrammetic representation is given below,

Substitute the values of b=a+3andc=a+4 in the above equation to get the following,

c2=a2+b2(a+4)2=a2+(a+3)2

Since (a+b)2=a2+2ab+b2 then the above equation the following,

(a+4)2=a2+(a+3)2a2+8a+16=a2+a2+6a+9a2+8a+16=2a2+6a+9a2+8a+162a26a9=0a2+2a+7=0

Then multiply the above equation by 1 on both sides to get the following,

1(a2+2a+7)=1×0a22a7=0

The general form of the quadratic equation is given below,

ax2+bx+c=0

Where a is the number multiplied by x2, b is the number multiplied by x, and c is the constant term.

The solution for ax2+bx+c=0 when a0 is given below,

x=b±b24ac2a(1)

Compare the given equation with general equation by substituting x=a to get the following,

ax2+bx+c=0x22x7=0

Therefore,

a=1,b=2andc=7

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