Correct Option: B

=	x² +	1	=		x +	1		²	- 2
		x²				x
		2				2

3a² + 3b² + 3c² = (a + b + c)²
⇒ 3a² + 3b² + 3c² = a² + b² + c² + 2ab + 2bc + 2ac
⇒ 3a² + 3b² + 3c² – a² – b² – c² – 2ab – 2bc – 2ac = 0
⇒ 2a² + 2b² + 2c² – 2ab – 2bc – 2ac = 0
⇒ a² + b² – 2ab + b² + ² – 2bc + a² + c² – 2ac = 0
⇒ (a – b)² + (b – c)² + (c – a)² = 0
⇒ a – b = 0 ⇒ a = b
b – c = 0 ⇒ b = c
c – a = 0 ⇒ c = a
∴ a = b = c

Correct Option: D

3a² + 3b² + 3c² = (a + b + c)²
⇒ 3a² + 3b² + 3c² = a² + b² + c² + 2ab + 2bc + 2ac
⇒ 3a² + 3b² + 3c² – a² – b² – c² – 2ab – 2bc – 2ac = 0
⇒ 2a² + 2b² + 2c² – 2ab – 2bc – 2ac = 0
⇒ a² + b² – 2ab + b² + ² – 2bc + a² + c² – 2ac = 0
⇒ (a – b)² + (b – c)² + (c – a)² = 0
⇒ a – b = 0 ⇒ a = b
b – c = 0 ⇒ b = c
c – a = 0 ⇒ c = a
∴ a = b = c

As the lines have equal intercepts.
∴ Equation of line is x + y = a
∴ Slope = –1

Correct Option: C

As the lines have equal intercepts.
∴ Equation of line is x + y = a
∴ Slope = –1

Let three numbers in A.P. be a – d, a and a + d respectively. According to the question, a – d + a + a + d = 30

Correct Option: C

Let three numbers in A.P. be a – d, a and a + d respectively. According to the question, a – d + a + a + d = 30

Correct Option: B