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Question

Solve each of the following quadratic equations: 
(i) 1x11x+5=67,x1,5
(ii) 12x31x5=119,x32,5


Solution

(i) 1x11x+5=67

 (x+5x+1)(x1)(x+5)=67

 6(x1)(x+5)=67

 6×76=x2+5xx5

 7=x2+4x5

 x2+4x12=0

 x2+(62)x12=0

 x2+6x2x12=0

 x(x+6)2(x+6)=0

 (x+6)(x2)=0

When 
 x+6=0x=6

and 
 x2=0x=2

x= 2 and -6


(ii) 12x31x5=119
 
 x5+2x3(2x3)(x5)=109

3x82x210x3x+15=109
 
3x82x213x+15=109

Cross multiply to get,      

10(2x213x+15)=9(3x8)

20x2130x+150=27x72

20x2157x+222=0

Factorise and solve,       

20x2120x37x+222=020x(x6)37(x6)=0 

(x6)(20x37)=0

x=6,3720

values of x are 6 and 3720


Mathematics
Secondary School Mathematics X
Standard X

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