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An Old Puzzle…

January19

I remember when I was doing Stage I Mathematics that our text (Principles of Mathematics by Carl Allendoerfer and Cletus Oakley!) contained a puzzlement something like this;

“I will prove that 2 = 1.  Your job is to show why such a logical proof could possibly be wrong.  It isn’t sufficient to point out that the answer is ridiculous.”

a   =a2   =a2 – b2   =

(a – b)(a + b)   =

a + b   =

2b   =

2   =

 b ab ab – b2

 b(a – b)

 b

 1b

 1

definition, multiply both sides by asubtract b2

factor

cancel like factors*

since a = b

divide by b

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Post Support

10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020

NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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