Q. 71

Solve each of the following quadratic equations:

3(x + 2) + 3 - x = 10

Answer :

Given: 3(x + 2) + 3 - x = 10

- - - - - - - - (1)


Let 3x = y - - - - - - - - - - (2)


substituting for y in (1)


9y2 - 10y + 1 = 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 = 9 b = - 10 c = 1


= 9.1 = 9


And either of their sum or difference = b


= - 10


Thus the two terms are - 9 and - 1


Sum = - 9 - 1 = - 10


Product = - 9. - 1 = 9


9y2 - 9y - 1y + 1 = 0


9y(y - 1) - 1(y - 1) = 0


(y - 1) (9y - 1) = 0


(y - 1) = 0 or (9y - 1) = 0


y = 1 or y = 1/9


3x = 1 or 3x = 1/9


On putting value of y in equation (2)


3x = 30 or 3x = 3 - 2


x = 0 or x = - 2


Hence the roots of equation are 0, - 2


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