SiNGTvK Equations. 85 



Clearing of fractions, 



whence ^=4. (6) 



2 2 



75. Solve x== — — — f- -r. . - . 



.r + V 2-{-x^ X— sj 2-^-x' 



16. Solve \/ x-\- sj 2-\-x=^ — — -—=. . 



//. Solve V 5-^ + 10= V 5-^+ 2. 



iS. Solve V 1 4--^'+ V I + .r + \/ 1 + r= V i — ^'- 



19. Solve ^+4^-=r-+^/- 

 x — s/ x"" — 9 



Rationalize the denominator of the fraction. 



15. Equations which can be Solved as Quadratics. The 

 method employed in the solution of quadratic equations will some- 

 times enable us to solve equations of other degrees, or even irra- 

 ttonal equations. Thus consider the equation 



3-^— 5-^^ + 4=2. (\) 



Multiply both members by four times coefficient of x^ and add the 

 square of the coefficient of x^ to each side, as in the solution of a 

 quadratic equation. It then becomes 



36;!::^— 6o,r^-f25=r. (2) 



The left-hand member is now a perfect square. Whence, extract- 

 ing the square root of both members, equation (2) becomes 



whence ji'^= i or |. 



Therefore Ji= -f i or — i or -f Vl or — \/| . 



As another example consider the equation 



\s/ X +3A=4. (\) 



Put r= sf X, whence it is seen that (\) becomes 



4.^+3.1"= 4- i'^) 



Solving this quadratic we find 



^'=1 or — 2. 

 Whence, since i'= sf x 



sj x=\ or — 2. 

 Therefore .^"==| or 4. 



These examples suggest the following theorems : 



