Quadratics - Completing the Square

[ProPM]

Hi,

The question asks: Use the method of completing the square to express the solutions to each of these quadratic equations in the form a ± b √n, where a and b are rational and n is an integer:

y² - 2y - 1 = 0
(y-1)² - 2 = 0
(y-1)² = 2
y = 1 + √2

I know how to solve but I don't know how to recognize a and b in my answer.

Can anyone please explain?

Thanks

 

[Mark44]

Hi,

The question asks: Use the method of completing the square to express the solutions to each of these quadratic equations in the form a ± b √n, where a and b are rational and n is an integer:

y² - 2y - 1 = 0
(y-1)² - 2 = 0
(y-1)² = 2
y = 1 + √2

Your only mistake is that the last line should be
y = 1 ± √2, which is the same as 1 ± 1√2

Here a = 1, b = 1, and n = 2

I know how to solve but I don't know how to recognize a and b in my answer.

Can anyone please explain?

Thanks

 

[ProPM]

Ok, thanks Mark 44.