Statement-1 (A): (a+b+c)^2+(a-b+c)^2+2 (b^2-a^2-c^2-2 a c )=2 b S… - Vidyadip

MCQ

Statement-1 (A): $\sqrt{(a+b+c)^2+(a-b+c)^2+2\left(b^2-a^2-c^2-2 a c\right)}=2 b$
Statement-2 (R): $(x+y+z)^2=x^2+y^2+z^2+2(x y+y z+z x)$

✓
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
B
Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
C
Statement-1 is True, Statement-2 is False.
D
Statement-1 is False, Statement-2 is True.

✓

Answer

Correct option: A.

Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.

(a)
Statement-2 is true, being a standard formula, using statement-2, we obtain
$(a+b+c)^2+(a-b+c)^2+2\left(b^2 \quad a^2-c^2-2 a c\right)=2\left(a^2+b^2+c^2+2 a c\right)+2\left(b^2-a^2-c^2-2 a c\right)=4 b^2$
$\therefore \sqrt{(a+b+c)^2+(a-b+c)^2+2\left(b^2-a^2-c^2-2 a c\right)}=2 b$

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