5 - 25 pattern

Algebra Level 2

It is observed that for any square of integer that ends with 5, the answer would be an integer that ends with 25. For examples: $15^2 = 225$ and $25^2 = 625$ .

Assuming the integer before 5 (on the LHS of equation) is assigned as $x$ , and the integer before 25 (on the RHS of equation) is $f(x)$ . Find function $f(x)$ .

f(x) = x (x + 1)

f(x) = 4x - 2

f(x) = 10x - \frac 4x

f(x) = 2x^3 - x

1 solution

Cl Chong
Jun 15, 2018

General equation would be:

(10x + 5)^2 = [100 * f(x)] + 25;

Expanding LHS:

(10x + 5)^2 = 100x^2 + 100x + 25 = 100 * (x^2 + x) + 25

Thus, f(x) = (x^2 + x) = x (x+1).

5 - 25 pattern

1 solution

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