uniuyo mth 111 exercise 2.4. Question number 1

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20180113

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uniuyo mth 111 exercise 2.4. Question number 1





In question number one we are ask to solve by factoring. Here are the solutions:

(i)
 x2-12=0
Factorizing gives:
x(x-12/x)=0
x-12/x=0
x=12/x
x2=12
x=+√12 or -√12
x=+2√3 or -2√3

(ii)
48-3x2=0
Divide through by 3;
16-x2=0
Rearranging gives;
x2-16=0
(x+4)(x-4) =0   (sum of 2 squares)
x+4=0 or x-4=0
x=-4 or 4

(iii)
x2=2x
Rearranging gives;
x2-2x=0
Factorizing gives;
x(x-2)=0
x-2=0
x=2

(iv)
2x2+6x=0
Dividing through by 2 gives;
x2+3x=0
Factorizing gives;
x(x+3)=0
x+3=0
x=-3

(v)
3x2+30x+72=0
Dividing through by 3 gives;
x2+10x+24=0
i.e.  x2+6x+4x+24=0
Factorizing gives;
x(x+6)+4(x+6)=0
i.e.  (x+4)(x+6)=0
x+4=0 or x+6=0
x=-4 or -6

(vi)
1/4(x-1)2-(x-1) -3=0
Let x-1=p
i.e.  p2/4-p-3=0
Multiplying through by 4 gives;
p2-4p-12=0
i.e.  p2+2p-6p-12=0
Factoring gives;
p(p+2)-6(p+2)=0
i.e.  (p-6) (p+2)=0
p-6=0 or p+2=0
p=6 or -2
Since x-1=p, we have that;
x-1=6 or x-1=-2
x=6+1 or x=-2+1
x=7 or x=-1
x=7 or -1

(vii)
Will be updated soon.

(viii)
Missing from the text.

(ix)
2x2-1=0
Dividing through by 2 gives; x2-1/2=0
Factorizing gives;
x(x-1/2x)=0
x-1/2x=0
x=1/2x
2x2=1=0
x2=1/2
x=-1/√2 or +1/√2

End of question 1 for exercise 2.4. Feel free to post your comments and reactions .



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