Question

Solve 3(a+1)^2 +2=11 with 2 different methods

Answer 1

`a = - 1 - √(3) \: or \: a = - 1 + √(3)`

Explanation:

We want to solve

`3 {(a + 1)}^(2) + 2 = 11`

with two different methods.

Subtract 2 from both sides:

`3 {(a + 1)}^(2) = 11 - 2 \\ 3 {(a + 1)}^(2) = 9`

Divide through by 3

`{(a + 1)}^(2) = 3`

Take square root:

`a + 1 = \pm √(3)`

`a = - 1\pm √(3)`

`a = - 1 - √(3) \: or \: a = - 1 + √(3)`

Method 2:

The given equation is

`3 {(a + 1)}^(2) + 2 = 11`

Expand

`3( {a}^(2) + 2a + 1) + 2 = 11`

Subtract 11

`3( {a}^(2) + 2a + 1) - 9 = 0`

Divide through by 3

`{a}^(2) + 2a + 1 - 3 = 0 \\ {a}^(2) + 2a - 2 = 0`

Use the quadratic formula:

`a = \frac{ - 2 \pm \sqrt{ {2}^(2) - 4 * 1 * - 2} }{2 * 1}`

`a = ( - 2 \pm √( 12) )/(2)`

`a = ( - 2 \pm2 √(3) )/(2)`

`a = - 1 \pm√(3)`

`a = - 1 - √(3) \: or \: a = - 1 + √(3)`