if a+b+c=2s then prove that (s-a) ²+ (s-b) ²+(s-c) ²=a²+b²+c²-s²
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Step-by-step explanation:
- given:a+b+c=2s
- LHS=(s-a)²+(s-b)²+(s-c)²
- =s²+a²-2as+s²+b²-2bs+s²+c²-2cs
- =3s²+a²+b²+c²-2s(a+b+c)
- =3s²+a²+b²+c²-(2s*2s)
- =a²+b²+c²-4s²+3s²
- =a²+b²+c²-s²=RHS
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