SOLUTIONS TO THE EXEBCisES.] MATHEMATICS. ALGEBRA. 



607 



Let the three numbers bo -, x, and xy ; then by the 

 question 



5 + x + xy = 35 . . . (1), 



and x : xy ? : : 2 : 3, .-. Zx = 2(xy |). 



2 ' 



/. 3 = 2y . . . (2), 



. . 3y = 2y 2 2, . . 2y 2 3y = 2, 

 Rule IL, page 474, 4y 3 = V(10 + 9) 



3 + 5 

 ' ^ = -"y- " 2 > or |. 



Hence, (1) becomes 



I + i + 2o; = 35, or 2* + x | = 35, 



that is, 3.t z = 35, or IJa; = 35, 



.-.x = 10, or, 23J. 

 Hence the numbers are either 



6, 10, and 20 ; or 46|, 23}, and llf, 

 both of which sets satisfy the conditions of the question. 



EXTRACTION OF THE SQUARE ROOT. EXAMPLES FOR EXEBCISE. PAGE 482 



2* + 24) 4jr+44 



2. 



12** + 4i 



9x< + 12x + 34*' + 20* + 25)3*' + 2-r + 5 



12x+ 



6** + 4* + 5) 30* J + 20* + 25 

 30* 3 + 20* + 25 



2** 4 



4* 3 +8* 5 4* + 4 

 4* 3 +&r 4*+4 



_ 4i + 10* 4*> 



2* 1 



6*' 4*> 

 6* 



8* 1 1 



6. 4** + G*>+ + 15* + 25(2*' 



4*' 



6*+ 



' The ttr 1 In the above square U of no ralne, end has oeen retained solely to indicate the succcssire diminution in the Tlue of the exponents of x.-l'.n. 



