solve bycompleting square method 3x^2 +2x-1=0
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According to the question,
3x²+2x-1=0
3x²+2x=1
Dividing by coefficient of x, that is 3, on both sides, we get:
x²+2/3x=1/3
1/2 of coefficient of x= 1/2*2/3=1/3
Adding (1/3)²on both sides, we get
x²+2/3x+(1/3)²= 1/3+ (1/3)²
x²+ 2*x*1/3+(1/3)²=1/3+(1/9)
The left hand side is of the form (a+b)²= a²+2ab+b², where a=x and b=1/3
Now,
(x+1/3)²=1/3+1/9
Taking L.C.M on Right Hand Side, we get
(x+1/3)²=(3+1)/9
(x+1/3)²=4/9
Now, two cases arise.
x+1/3= +√4/9, and x+1/3= -√4/9
Case 1:
x+1/3= +√4/9
x+1/3= 2/3
x= 2/3-1/3
x=1/3
Case 2:
x+1/3 = -√4/9
x+1/3= -2/3
x= -2/3-1/3
x=-3/3
x= -1
Therefore, values of x are -1 and 1/3.
I hope this helps you.
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