Here a + b = 2c
Now checking each options individually
Option (a)
a2 + 2ac = b2 + 2bc
putting a = 2c -b
(2c-b)2 + 2(2c-b)c = b2 + 2bc
4c2 -4bc + b2 + 4c2 - 2bc = b2 + 2bc
8c2 - 6bc + b2 ≠ b2 + 2bc.
So option (a) does not satisfy
Option (b)
a2 - 2bc = b2 - 2ac
putting a= 2c - b
(2c -b)2 -2bc = b2 -2(2c -b)c
4c2 - 4bc + b2 - 2bc = b2 -4c2 + 2bc
4c2 - 6bc + b2 ≠ b2 - 4c2 + 2bc
So option (b) does not satisfy
Option (c)
a2 + 2bc = b2 + 2ac≠
Putting a = 2c - b
(2c-b)2 + 2bc = b2 + 2c(2c-b)
4c2 - 4bc + b2 + 2bc = b2 + 4c2 -2bc
4c2 - 2bc + b2 = b2 + 4c2 - 2bc
So option (c) satisfies.
Option (d)
a2 - ac = b2 - bc
putting a=2c-b;
(2c-b)2 - (2c-b)c = b2 -bc
4c2 - 4bc +b2 - 2c2 + bc = b2 -bc
2c2 -3bc +b2 ≠b2 -bc
Option (d) does not satisfy.
Study Notes
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