If 3x² - 2x + 7 = 0, then (x - 1/3)² = ?

Solution:

Given, the equation is 3x² - 2x + 7 = 0

We have to find (x - 1/3)²

Rewriting the given equation,

3x² - 2x = - 7

Let us complete the square, by making the LHS a trinomial.

Dividing by 3 throughout, we get

x² - 2x/3 = - 7/3

Adding 1/9 on both sides, we get

x² - 2x/3 + 1/9 = -7/3 + 1/9

We know, (a - b)² = a² - 2ab + b²

So, (x - 1/3)² = -20/9

Therefore, the value of (x - 1/3)² is -20/9.

If 3x² - 2x + 7 = 0, then (x - 1/3)² = ?

Summary:

If 3x² - 2x + 7 = 0, then (x - 1/3)² = -20/9.