IV = V?

Algebra Level 2

I will attempt to prove that 4=54=5. Try and spot my mistake in the following steps:

A. Starting with the equality 1636=2545,16-36=25-45, B. we can add 814\frac{81}{4} to both sides of this equality without changing anything: 1636+(814)=2545+(814).16-36+\left( \frac { 81 }{ 4 } \right) =25-45+\left( \frac { 81 }{ 4 } \right). C. Using the perfect square trinomial properties, we can rewrite this equality as follows: (492)2=(592)2.{ \left( 4-\frac { 9 }{ 2 } \right) }^{ 2 }={ \left( 5-\frac { 9 }{ 2 } \right) }^{ 2 }. D. Taking the square root of both sides, 492=592.4-\frac { 9 }{ 2 } =5-\frac { 9 }{ 2 }. E. Adding 92\frac { 9 }{ 2 } to both sides gives 4=5.4=5.

Which step contains the error?

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