This video demonstrates a classic mathematical fallacy where the presenter attempts to prove that 2 equals 1 through algebraic manipulation. The proof begins with a = 1 and b = 1, then multiplies both sides by a, subtracts b² from both sides, factors the difference of squares, and finally divides both sides by (a - b). The critical error occurs when dividing by (a - b), which equals zero since a = b. This division by zero is mathematically invalid and leads to the false conclusion that 2 = 1. The video illustrates why division by zero must be avoided in algebraic proofs, as it can produce logically impossible results.
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True? #maths #gcsemaths #sat #highschoolmath #gcse #matheducation #exam #study #school #fypシ追加:
I will mathematically prove to you that 2 is equal to 1. Now I'm going to start off with a equal 1 and b is equal to 1.
We could all establish that a is equal to b 1 is equal to 1. Then what I'm going to do is I'm going to multiply both sides by a. So multiply this by a multiply this by a. a * a will give me a to the second power. And then on the right side b * a same as ba or a b. And then what I'm going to do is I'm going to minus b ^ 2 on both sides. What happens on the left side is I'm left with a^ 2us b^2. We'll deal with that in a second. On the right side, it's a b minus b to the 2. a^ squareus b square.
Well, we know that's the difference of squares. That factors out into a + b * a minus b. Difference of squares. And on the right side, I see that a b and b ^ 2 can factor out a b. So b * what is a b?
That's just a. B * what is ne 2? That's just minus b. In this case, I see that a minus b and a minus b are both common on the left and right. So I'm going to divide that on both sides. Divide by a minus b. a minus bs cancel out. A minus b cancel out. So on the left side I'm just left of a plus b. On the right side I'm just left of b. So in that case 1 plus 1 is equal to 1.
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