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Home » You Won’t Believe What 18 Is — It’s Just 1.8 in Decimal Form! - Blask

You Won’t Believe What 18 Is — It’s Just 1.8 in Decimal Form! - Blask

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 5Question: Find all functions $ f: \mathbb{R} o \mathbb{R} $ such that $ f(x + y) + f(x - y) = 2f(x) + 2f(y) $ for all real numbers $ x $ and $ y $.

📌 Solution: Assume $ f $ is a quadratic function. Let $ f(x) = ax^2 + bx + c $. Substituting into the equation:

📌 a(x + y)^2 + b(x + y) + c + a(x - y)^2 + b(x - y) + c = 2(ax^2 + bx + c) + 2(ay^2 + by + c).

📌 2a x^2 + 2a y^2 + 2b x + 2c = 2a x^2 + 2a y^2 + 2b x + 2b y + 4c.

📌 Equating coefficients: $ 2c = 2b y + 4c $ for all $ y $, which implies $ b = 0 $ and $ c = 0 $. Thus, $ f(x) = ax^2 $. Verification confirms this satisfies the equation. Hence, all solutions are quadratic functions of the form $ f(x) = kx^2 $.

📌 oxed{f(x) = kx^2 ext{ for some constant } k}

📌 Question: Let $ a $ and $ b $ be complex numbers such that $ |a| = |b| = 1 $ and $ a

📌 eq b $. Find the value of $ rac{a + b}{a - b} + rac{a - b}{a + b} $.

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\frac{(a - 2d) + (a - d) + a + (a + d) + (a + 2d)}{5} = a = 22
The total difference between highest and lowest is:
The third sample has nutrient level $ a = 22 $.
Thus, the nutrient level at the third sample is $ \boxed{22} $.
Question: If $ x + y = 10 $ and $ x^2 + y^2 = 58 $, find $ x^3 + y^3 $...
x^3 + y^3 = (x + y)^3 - 3xy(x + y)
$ x + y = 10 $, $ x^2 + y^2 = 58 $
Recall:
Now substitute into the identity:
x^3 + y^3 = (10)^3 - 3(21)(10) = 1000 - 630 = 370

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