If a²+b²+c²-ab-bc-ca=0 ,prove that a=b=c
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Answered by
2
if a,b,c=1
then a=1*1=1
b=1*1=1
c=1*1=1
a+b+c=1*1+1*1+1*1=3
-1*1-1*1-1*1=-3
3=-3=0
hence its proved
then a=1*1=1
b=1*1=1
c=1*1=1
a+b+c=1*1+1*1+1*1=3
-1*1-1*1-1*1=-3
3=-3=0
hence its proved
Answered by
2
Step-by-step explanation:
We have,
a² + b² + c² - ab - bc - ca = 0
=> 2a² + 2b² + 2c² - 2ab - 2bc - 2ca = 2 × 0
=> (a² - 2ab + b2) + (b² - 2bc + c²) + (c² - 2ac +
a²) = 0
=> (a-b)² + (b-c)² + (c-a)² = 0
=> a - b = 0, b - c = 0, c - a = 0
=> a = b, b = c and c = a => a = b = c
• Therefore, a = b = c
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