Question

Which equation has the same solution as this equation?

Answer 1

3rd Option is correct.

Explanation:

Given Equation:

x² - 16x + 12 = 0

First We need to find solution of the given equation.

x² - 16x + 12 = 0

here, a = 1 , b = -16 & c = 12

`x=(-b\pm√(b^2-4ac))/(2a)`

`x=(-(-16)\pm√((-16)^2-4(12)))/(2)`

`x=(16\pm√(256-48))/(2)`

`x=(16\pm√(208))/(2)`

`x=(16\pm4√(13))/(2)`

`x=8+2√(13)\:\:andx=8-2√(13)`

Now,

Option 1).

( x - 8 )² = 144

x - 8 = ±√144

x - 8 = ±12

x = 8 + 12 = 20 and x = 8 - 12 = -4

Thus, This is not correct Option.

Option 2).

( x - 4 )² = 4

x - 4 = ±√4

x - 4 = ±2

x = 4 + 2 = 6 and x = 4 - 2 = 2

Thus, This is not correct Option.

Option 3).

( x - 8 )² = 52

x - 8 = ±√52

x - 8 = ±2√13

x = 8 + 2√13 and x = 8 - 2√13

Thus, This is correct Option.

Option 4).

( x - 4 )² = 16

x - 4 = ±√116

x - 4 = ±4

x = 4 + 4 = 8 and x = 4 - 4 = 0

Thus, This is not correct Option.

Therefore, 3rd Option is correct.