Anjurie

Linear Algebra: Vectors

Show that |a+b|^2 + |a-b|^2 = 2|a|^2 +|b|^2
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Finguine_L
|a-b|^2 will expand just like (a-b)^2. |a+b|^2 will provide two reulsts. one would be (a+b)^2 and would be -(a+b)^2. Adding these two will generate right side of equation.
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Benny_BB
Right hand side in equation is wrong. It is 2(|a|^2 +|b|^2).
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Anita_fj
In this simple linear algebra problem, take left side of equation ​ |a+b|^2 + |a-b|^2 |a+b|^2 = |a|^2 + |b|^2 + 2|a||b| either a>=b or a<b |a-b|^2 = |a|^2 + |b|^2 - 2|a||b| either a>=b or a<b ​ Add these two and result is: ​ 2(|a|^2+|b|^2) = Right hand side
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