37<> 



^LGEBHA. 



15. To find four numbers in geometrical progrossion, 

 whpse sum is 15, ami the $um of their squares 83/. 



Alls. I, 2, 4 and 8. 



1(5. Given x' 

 value of X. 



_1- ^ "^ 



zz — ; to find the 

 a 



Ans. .vrz 1^^ + v/^— ■ 

 '4 * 



CUBIC AND HIGHER EQUATIONS- 



A CUBIC EQUATION, or equation of the third degree or 

 power, is one, that contains the third power of the un- 

 known quantity : as .v^ — ax^'\'^x'zzc. 



A biquadrat'tc^ or double quadratic, is an equation, that 

 contains the fourth power of the unknown quantity : as 

 9i * — ax ^ -j-^^ * — cxzzd. 



An equation of the fifth power, or degree, is one, that 

 contains the fifth power of the unknown quantity : as ^^ 

 "■^ax "* -^bx ^ — cx ' -J-^.v zzf . 



An equation df the sixth powery or degree, is one, that 

 contains the sixth power of the unknown quantity : as ^* 

 — r^^ ^ '\-bx ^ cx ^ -i-dx * ex ZZf. 



And so on, for all other higher powers. Where it is to 

 be noted, however, that all the powers, or terms, in the 

 equation are supposed to be freed from surds, or fractional 

 exponents. 



There are various particular rules for the resolution of 

 cubic and higher equations ; but they may be all easily re- 

 solved by the following rule of Double Position. 



RULE. 



