# IV = V?

Algebra Level 2

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

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

Which step contains the error?

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