GreenlightTestPrep wrote:

Which of the following is NOT a root of the equation (x² + x - 20)² - 2(x² + x - 20) - 63 = 17

A) -6

B) -4

C) 3

D) 4

E) 5

*Note: there are at least 3 different solutions possible

APPROACH 1: Plug in each answer choice to see which value does NOT satisfy the equation (slow but...)

For example, C) x =

3We get: (

3² +

3 - 20)² - 2(

3² +

3 - 20) - 63 = 17

Evaluate: (-8)² - 2(-8) - 63 = 17

Simplify: 64 - 16 - 63 = 17

Works! So, x =

3 is a valid solution

Try D) x =

4We get: (

4² +

4 - 20)² - 2(

4² +

4 - 20) - 63 = 17

Evaluate: (0)² - 2(0) - 63 = 17

Simplify: -63 = 17

Works! So, x =

4 is NOT a valid solution

Answer: D

------------------------------------------------

APPROACH 2: Let

k = x² + x - 20Now replace x² + x - 20 with k to get: k² - 2k - 63 = 17

Subtract 17 from both sides to get: k² - 2k - 80 = 0

Factor: (k - 10)(k + 8) = 0

So, either k = 10 or k = -8

Now replace k with x² + x - 20 to get:

x² + x - 20 = 10 and x² + x - 20 = -8

Take: x² + x - 20 = 10

Rearrange: x² + x - 30 = 0

Factor: (x + 6)(x - 5) = 0

Solutions: x = -6 and x = 5

Take: x² + x - 20 = -8

Rearrange: x² + x - 12 = 0

Factor: (x + 4)(x - 3) = 0

Solutions: x = -4 and x = 3

ALL SOLUTIONS: x = -6, 5, -4 and 3

Answer: D

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APPROACH 3: Examine: x² + x - 20

Factor to get: (x + 5)(x - 4)

Notice that, when x =

4, (x + 5)(x - 4) = (4 + 5)(

4 - 4) = 0

So, when x =

4, we get: (0)² - 2(0) - 63 = 17

When we simplify, we get: -63 = 17

In other words, x =

4 is NOT a solution to the original equation.

Answer: D

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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