Two Equals One

An Advanced Mathematics Lesson Starter Of The Day

Consider two positive numbers \(a\) and \(b\) that are equal:$$ a = b $$
Multiply both sides of this equation by \(a\),$$ a^{2}=ab $$
Subtract \(b^2\) from both sides. $$ a^{2}-b^{2}=ab-b^{2} $$
Factorise both sides$$ (a-b)(a+b)=b(a-b) $$
Divide both sides by \( (a - b) \).$$a+b=b $$
As \( a = b \) substitute \(b\) for \(a\).$$ b+b=b $$
Collect like terms$$ 2b=b $$
Divide both sides by \( b \).$$2 = 1 $$
How can this be?$$???$$

Topics: Starter

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