Question

Find the value of a*2+b*2+c*2-ab-bc-ca when a-b=2,b-c=3,c-a=4

Answer 1

HELLO

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a^2 + b^2 + c^2 – ab – bc – ca = 0

Multiply both sides with 2,

we get

2( a^2 + b^2 + c^2 – ab – bc – ca) = 0

⇒ 2a^2 + 2b^2 + 2c^2 – 2ab – 2bc – 2ca = 0

⇒ (a^2 – 2ab + b^2) + (b^2 – 2bc + c^2) + (c^2 – 2ca + a^2) = 0

⇒ (a –b)^2 + (b – c)^2 + (c – a)^2 =0

put the value a-b=2,b-c=3,c-a=4 in (a –b)^2 + (b – c)^2 + (c – a)^2

⇒ 2^2 + 3^2 + 4^2

⇒ 4 + 9 + 16

⇒ 29

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THANKS ☺️