Question : Prove that : Q -a2+b2+c22=2bc-a2+b2+c2 2bc+a2-b2-c2 - Maths - Algebraic Expressions and Identities

Question

Question :

Prove that :

Q   - a 2 + b 2 + c 2 2 = 2 b c - a 2 + b 2 + c 2   2 b c
+ a 2 - b 2 - c 2

Sanjari Kalantri · Accepted Answer

Dear Student,

To prove: b2 - -a2 + b2 + c22c2 = 2bc - a2 + b2 + c22bc + a2 - b2 - c24c2Proof: LHS = b2 - -a2 + b2 + c22c2= b + -a2 + b2 + c22cb - -a2 + b2 + c22c       ∵ x2 - y2 = x + yx - y= 2bc + -a2 + b2 + c22c2bc - -a2 + b2 + c22c= 2bc - a2 + b2 + c2 2bc + a2 - b2 - c24c2= RHSHence, proved

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Question : Prove that : Q . - a 2 + b 2 + c 2 2 = 2 b c - a 2 + b 2 + c 2 2 b c + a 2 - b 2 - c 2

Question :

Prove that :

$Q . {(- a^{2} + b^{2} + c^{2})}^{2} = (2 b c - a^{2} + b^{2} + c^{2}) (2 b c + a^{2} - b^{2} - c^{2})$