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Chapter 9: Q. 410 (page 1108)

In the following exercises, solve.

(a) r-1-r=-1

(b)role="math" localid="1647990004799" z+100-z+10=0

Short Answer

Expert verified

Part (a) : r=1,2

Part (b) : z=0,21

Step by step solution

01

Part (a) Step 1. Given information.

An equation is given asr-1-r=-1.

02

Part (a) Step 2. Solution.

Isolate radical to one side, take square and simplify.

r-1-r=-1r-1-r+r=-1+rr-1=r-1(r-1)2=(r-1)2 r-1=r2-2r+10=r2-2r+1-r+10=r2-3r+2r2-3r+2=0r2-r-2r+2=0r(r-1)-2(r-1)=0(r-1)(r-2)=0r=1orr=2

03

Part (b) Step 1. Solution.

To solve z+100-z+10=0.

Isolate radical to one side, take square and simplify.

z+100-z+10=0z+100-z+10+z-10=0+z-10z+100=z-10(z+100)2=(z-10)2 z+100=z2-20z+1000=z2-20z+100-z-1000=z2-21zz2-21z=0z(z-21)=0z=0orz=21

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