If $ a^{2}+b^{2}+c^{2}+84 = 4(a-2b+4c),$ then $\sqrt{ab-bc+ca}$ is equal to :
Answer & explanation
Correct answer: option 4
a2 + b2 + c2 + 84 = 4(a - 2b + 4c)
Arrange the equation in this format given below,
= a2 + b2 + c2 + 84 - 4a + 8b -16c = 0
= a2 - 4a + 4 +b2 + 8b + 16+ c2 - 16c + 64 = 0
= (a – 2)2 + (b + 4)2 + (c-8)2 = 0
Now,
a = 2
b = -4
c = 8
$\sqrt{ab-bc+ca}$ = $\sqrt{2 \times -4 - (-4) \times 8 + 8 \times 2}$
$\sqrt{ab-bc+ca}$ = $\sqrt{40}$ = $2\sqrt{10}$