ID: f65288e8
(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Advanced Math)
Comment: Learn to recognize perfect squares (and differences of squares).
Method 1: If you recognize x^2 + 10x + 25 as the perfect square (x + 5)^2, you can quickly rearrange and either use logic or work out the arithmetic to arrive at the answer.
1/(x + 5)^2 = 4
1 = 4(x + 5)^2
1/4 = (x + 5)^2
1/2 = x + 5
The correct answer is (A).
Method 2: You can use Desmos to graph the solution for x and then answer the question.
Method 3: You can use the answer choices to corroborate known information, but it takes an extra step—namely, if x + 5 = {answer choice}, then x = {answer choice} - 5. Knowing that whatever value of x you derive must allow the fraction to equal 4, you can check each option. I will illustrate all four answers, even though I would stop at (A) for obvious reasons.
A. x = (1/2) - 5 = -4.5 or -9/2 --> 1/[(-9/2)^2 + 10(-9/2) + 25] = 1/[81/4 - 45 + 25] = 1/[81/4 - 20] =
1/[81/4 - 80/4] = 1/[1/4] = 4 √
B. x = (5/2) - 5 = -2.5 or -5/2 --> 1/[(-5/2)^2 + 10(-5/2) + 25] = 1/[25/4 - 25 + 25] = 1/[25/4] = 4/25 X
C. x = (9/2) - 5 = -0.5 or -1/2 --> 1/[(-1/2)^2 + 10(-1/2) + 25] = 1/[1/4 - 5 + 25] = 1/[1/4 + 20] =
1/[1/4 + 80/4] = 1/[81/4] = 4/81 X
D. x = (11/2) - 5 = 0.5 or 1/2 --> 1/[(1/2)^2 + 10(1/2) + 25] = 1/[1/4 + 5 + 25] = 1/[1/4 + 30] =
1/[1/4 + 120/4] = 1/[121/4] = 4/121 X
Because this method is less direct than either of the other two methods above, I would not recommend using it. At the same time, it does illustrate what a difference it makes to be presented with answer choices. In any case, the correct answer is (A).
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