Single Equations. 87 



But really 27 and —8 have each ///r^f different cube roots instead 

 of merely the onCvS we have written above. The full considera- 

 tion of this matter involves subjects somewhat more advanced, 

 and more than the mere statement above given will not be at- 

 tempted until Part II of the present work is reached. 



18. ExAMPLEvS. The following five are examples under the 

 theorem of Art. 16 : 



/ . Solve x^ -f 1 6x- =225. 

 2. Solve .^-^— 9-v'+8=o. 

 J . Solve 6x* — 3 5 = iiA ^ 



4. Solve Jt:=HH¥-^"''- 

 ^ . ^^.^"^ — 2\f X -\-x=o. 

 The following five are examples under the theorem of Art. 17. 



6. Solve -^■^-5V37— •* — 43- 



Process : Subtract 37 from each side of the equation, obtaining 



^^'— 37 + 5V37— -'^"=6 

 which may be written 



— ("37— -^'>> + 5V37— -^ — 6 

 or • ^37— -^y* — 5V37— -^"=— 6. 



Putting V for ^ t^'j — x this becomes 



Solving, >'=3 pr 2. 



That is s/ 2,']—x=-2) or 2 



whence 37— a"=9 or 4 



and .r=28 or 33. 



The same example may be treated by the method of Art. 1 1 . 



7. Solve .1''— V JT— 9= 21. 



8. Sol ve 2 V x^ — 5-V + 2 — x' + 8x = 3.1- — 7 8 . 



9. vSolve (^2.1''— 3.r-f i/=22a''— 33^-1- 1 1. 



10. Solve 4X" — ^x-\-20\/ 2xf' — 5jr-|-6=6.v-f 66. 

 The following. are examples of either the theorem of Art. 16 or 

 of Art. 1 7 : 



