533 MATHKM \ TICS. ALOEBK \. [SOLUTIONS TO TUB EXEI. 



Olbneut. 1G* + 24x> + 89*' + 60* + 100(4*' -f. 3* + 10 

 l&r .'.Root = 2*- + 5.r +5 



24*' + 9jr' 



BO.r' + CO.r+lOO 

 80*' + 60* +100 



SQUARE Boor or A BINOMIAL SUED. EXAMPLES FOB EXEBCIHE. PAOE 483. 



1. Put ^(19 + 8 -/3) = x + y, .: -/(19 8 V3) = * y. Taking the product, 

 V(361 192) =** y; that is, 13 = z y'. AUo, 



19 + 8^3 = ^ + 2jy +y, .' . ^9 = * + y' 



.. , 



..a = 16,.-.* = 4; y' = 3,.-.y= 



4; y' = 3,.-.y= 

 */3) = 4+ V3. 



2. ^(12 ^140) = ! y, .. V"(12+ ^140) =jr + y. Taking tlie product, 

 V(144 140) = x 1 y*j that is, 2 = JT* y*. 

 Also, 12 A/140 = jr 2xy + y', .' . 12=j' 



3. ^/(7 2 V10) = z-y, .'. /(? +2 >/10)=i + y. Taking the product, 

 v/(49 40) = ! /; that is, 3 = z* y 1 



Also, 7 2 V' 1 = x"- 2xy + y, .:T= 



.-. 10 = 2^, 4=2y 



.-. i' =5, .-.z=v'5; ^==2, .-.y = v 2 

 .-. \/(7 2V10) = V V 2. 



4. v/ (8 + y 39) = x + y, .-. v/ (8 v/ 39) = x y. Taking the product, 

 V (64 39)=** y-; that is, 5 = x y* 



Also, 8 + y/39=x a + 2xy + y 3 , .-. 8 = x'+y' 



.-.13= 2x 2 , 3=2y' 



: y 2 = - ' y=: 5 v/G 



5. ^ (76 _ 32 v/ 3) = x y, .'. V (76 + 32 v/ 3) = x + y. Taking the product, \/ (5776 3072) = z- y' j that is, 



52 = x j y 2 . 

 Also, 70 32 v/ 3 = x- Zry + y% .-._7_6 = j' + y" 



.-.128= Ix 1 , 24 = 2y'; 

 .-. *'= 64, .-. z = 8 ; > = 12, .-. y = 2 y/ 3, 

 ... ^ (76 32 v/3) = 8 2 V 3. 



6. V/O1 + 12v/ 5)=x + y, .'. \/(31 12 \/ 5)=* y. Taking the product, \/ (961 + 720; =.ac"- y-; that is, 



41 = x' y 5 . 



Also, 31 + 12 V 5 = *'- + 2xy + y', .'. 31 =x' + y 



.-.72= 2^-, 10 = 2y*-; 

 ..i5=3fi, .-.x = C; y-= 5, .-.y = v/ 5, 



To RATIONALISE BINOMIAL SUBDS. EXAMPLES FOB EXERCISE. PAGE 484. 

 1. Prove that 



3v/2 

 Multiplying numerator and denominator by 2 \/ 7 + 3 V 2, 



3 3(2v/7 + 3^2)_ 3 . x 



V 



28 18 



2. Prove that |- '- = - Multiplying the terms by 3 ^ 3, 



y/3) _ 



V 3 



