MCQ
$\sqrt{(a+b+c)^2+(a+b-c)^2+2\left(c^2-a^2-b^2-2 a b\right)}$ is equal to
- ✓2c
- B2a
- C2b
- Da + b + c
✓
Answer
Correct option: A.
2c
(a)
We find that,
$(a+b+c)^2+(a+b-c)^2+2\left(c^2-a^2-b^2-2 a b\right)$
$=2\left(a^2+b^2+c^2+2 a b\right)+2\left(c^2-a^2-b^2-2 a b\right)=2\left(2 c^2\right)=4 c^2$
$\therefore \quad \sqrt{(a+b+c)^2+(a+b-c)^2+2\left(c^2-a^2-b^2-2 a b\right)}=2 c$
We find that,
$(a+b+c)^2+(a+b-c)^2+2\left(c^2-a^2-b^2-2 a b\right)$
$=2\left(a^2+b^2+c^2+2 a b\right)+2\left(c^2-a^2-b^2-2 a b\right)=2\left(2 c^2\right)=4 c^2$
$\therefore \quad \sqrt{(a+b+c)^2+(a+b-c)^2+2\left(c^2-a^2-b^2-2 a b\right)}=2 c$
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