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\(\frac{(4.53-3.07)^2}{(3.07-2.15)(2.15-4.53)} + \frac{(3.07-2.15)^2}{(2.15-4.53)(4.53-3.07)} + \frac{(2.15-4.53)^2}{(4.53-3.07)(3.07-2.15)}\) is simplified to

Question and options

(4.53−3.07)2(3.07−2.15)(2.15−4.53)+(3.07−2.15)2(2.15−4.53)(4.53−3.07)+(2.15−4.53)2(4.53−3.07)(3.07−2.15)\frac{(4.53-3.07)^2}{(3.07-2.15)(2.15-4.53)} + \frac{(3.07-2.15)^2}{(2.15-4.53)(4.53-3.07)} + \frac{(2.15-4.53)^2}{(4.53-3.07)(3.07-2.15)} is simplified to
  1. 0
  2. 1
  3. 2
  4. 3

Answer and explanation

Correct answer: D - 3
Let a=4.53-3.07, b=3.07-2.15, c=2.15-4.53; a+b+c = 0. Expression = a^2/(bc)+b^2/(ca)+c^2/(ab) = (a^3+b^3+c^3)/(abc) = 3abc/abc = 3.

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