Question

solve bycompleting square method 3x^2 +2x-1=0​

Answer 1

Answer:

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.