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CUET
General Test
Quantitative Reasoning
Algebra
If $ a^{2}+b^{2}+c^{2}+84 = 4(a-2b+4c),$ then $\sqrt{ab-bc+ca}$ is equal to : |
$4\sqrt{10}$ $\sqrt{10}$ $5\sqrt{10}$ $2\sqrt{10}$ |
$2\sqrt{10}$ |
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 $\sqrt{ab-bc+ca}$ = $\sqrt{2 \times -4 - (-4) \times 8 + 8 \times 2}$ $\sqrt{ab-bc+ca}$ = $\sqrt{40}$ = $2\sqrt{10}$ |