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```
a 2 +b 2 +c 2 =ab+bc+ca then prove that a/b+c +b/c+a +c/b+a =3/2

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11 months ago

Vikas TU
13783 Points
```							Dear student a2 + b2 + c2 – ab – bc – ca = 0Multiply both sides with 2, we get2( a2 + b2 + c2 – ab – bc – ca) = 0⇒ 2a2 + 2b2 + 2c2 – 2ab – 2bc – 2ca = 0⇒ a2 + a2 + b2 + b2 + c2 + c2– 2ab – 2bc – 2ca = 0⇒ (a2 – 2ab + b2) + (b2 – 2bc + c2) + (c2 – 2ca + a2) = 0⇒ (a – b)2 + (b – c)2 + (c – a)2 = 0Since the sum of squares is zero, it means each term should be zero.⇒ (a – b)2 = 0,  (b – c)2 = 0, (c – a)2 = 0⇒ a – b = 0,  b – c = 0,  c – a = 0⇒ a = b,  b = c, c = a⇒ a = b = cPut this value in the equation , a/b+c +b/c+a +c/b+a =3/2Hope this will help Good Luck Cheers
```
11 months ago
Arun
25285 Points
```							 take it asa2+b2+c2-ab-bc-ca=0Multiply both sides with 2, we get2( a2 + b2 + c2 – ab – bc – ca) = 02a2 + 2b2 + 2c2 – 2ab – 2bc – 2ca = 0(a2 – 2ab + b2) + (b2 – 2bc + c2) + (c2 – 2ca + a2) = 0(a –b)2 + (b – c)2 + (c – a)2 = 0Since the sum of square is zero then each term should be zero(a –b)2 = 0,  (b – c)2 = 0, (c – a)2 = 0(a –b) = 0,  (b – c) = 0, (c – a) = 0a = b,  b = c, c = aa = b = c.therefore c+a/b=2 similarly all the terms = ½hence answer = 1/2+ ½ + ½ = 3/2
```
11 months ago
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### Course Features

• 101 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions