GMATPrepNow 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
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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
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