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zip code philadelphia pennsylvania united states - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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The sum of all real solutions to the equation \( |2x - 5| = |x + 3| \)...
Use the property \( |A| = |B| \Rightarrow A = B \) or \( A = -B \).
Case 1: \( 2x - 5 = x + 3 \Rightarrow x = 8 \)
Check: LHS = |16 - 5| = 11, RHS = |8 + 3| = 11 → valid.
Case 2: \( 2x - 5 = -(x + 3) \Rightarrow 2x - 5 = -x - 3 \Rightarrow 3...
Check: LHS = |4/3 - 5| = |-11/3| = 11/3, RHS = |2/3 + 3| = |11/3| = 11...
Sum = \( 8 + \frac{2}{3} = \frac{24}{3} + \frac{2}{3} = \frac{26}{3} \...
#### 26/3
A circle with center at (2, -3) passes through the point (5, 1). What...
Use distance formula:

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The roots of the original equation are $ u = 0, 4, 9 $. Their sum is:
+ 4 + 9 = 13.
Thus, the sum of the roots is
\boxed{13}.
Question: Let $ f(x) $ be a polynomial such that
f(x^2 + 2) = x^4 + 4x^2 + 2.
Find $ f(x^2 - 2) $.
Solution: We are given that
Let us denote $ y = x^2 + 2 $, so that $ x^2 = y - 2 $. Then
x^4 = (x^2)^2 = (y - 2)^2 = y^2 - 4y + 4.

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