plz give me correct answer
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Answer:
should be a square plus b plus a minus
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Answer:
Option C
Given:
a + b + c = 0; This can also be written as follows:
a + b = -c;
a + c = -b;
b + c = -a
(a+b)²/ab + (b+c)²/bc + (c+a)²/ca; This can also be written as follows:
(a+b)²/ab + (b+c)²/bc = -(c+a)²/ca
Solution:
(a+b)²/ab + (b+c)²/bc = -(c+a)²/ca
=⟩ (-c)²/ab + (-a)²/bc = -(-b)²/ca
=⟩ c²/ab + a²/bc = b²/ca
=⟩ c³ + a³/abc = b²/ca
=⟩ c³ + a³ = (b² × abc) / ca
=⟩ c³ + a³ = b³
=⟩ (c + a)³ - 3ac (c + a) = b³
=⟩ (-b)³ - 3ac (-b) = b³
=⟩ -b³ + 3abc = b³
=⟩ -b³ -b³ = -3abc
=⟩ -2b³ = -3abc
=⟩ 2b³ = 3abc
=⟩ 2b³/abc = 3
Therefore, (a+b)²/ab + (b+c)²/bc + (c+a)²/ca = 3
Explanation:
1. Since (a+b)²/ab + (b+c)²/bc + (c+a)²/ca can also be written as (a+b)²/ab + (b+c)²/bc = -(c+a)²/ca, therefore [(a+b)²/ab + (b+c)²/bc = -(c+a)²/ca] = [c³ + a³ = b³] and [(a+b)²/ab + (b+c)²/bc + (c+a)²/ca] = [c³ + a³ - b³].
2. When c³ + a³ = b³ is simplified, we get 2b³ = 3abc i.e., c³ + a³ - b³ = 3abc which is equal to (a+b)²/ab + (b+c)²/bc + (c+a)²/ca.
3. When abc is divided from both the sides we get 3 which is the required answer.
Hope you understood how I did. If this really helped uou, please mark me as Brainliest. Cheers :)
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