Q. 734.3( 7 Votes )

Solve each of the following quadratic equations:

22x - 3.2(x + 2) + 32 = 0

Answer :

Given: 22x - 3.2(x + 2) + 32 = 0

(2x)2 - 3.2x.22 + 32 = 0 - - - - (1)


Let 2x = y - - - - - - (2)


substituting for y in (1)


y2 - 12y + 32 = 0


Using the splitting middle term - the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 1 b = - 12 c = 32


= 1.32 = 32


And either of their sum or difference = b


= - 12


Thus the two terms are - 8 and - 4


Sum = - 8 - 4 = - 12


Product = - 8. - 4 = 32


y2 - 8y - 4y + 32 = 0


y(y - 8) - 4(y - 8) = 0


(y - 8) (y - 4) = 0


(y - 8) = 0 or (y - 4) = 0


y = 8 or y = 4


2x = 8 or 2x = 4


substituting the value of y in (2)


2x = 23 or 2x = 22


x = 2 or x = 3


Hence the roots of equation are 2, 3


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