Question
The sum of the total surface areas of two cubes is 1926
cm2. If the product of the length of their edges is 136 cm2, then find the difference (in cm) between the lengths of their edges.Solution
Let the length of the edges of the two cubes be ‘a’ cm and ‘b’ cm, respectively According to the question, 6a2 + 6b2 = 1926 Or, a2 + b2 = 1926/6 = 321 And, ab = 136 Using the formula, x2 + y2 = (x – y)2 + 2xy 321 = (a – b)2 + 2 × 136 Or, (a – b)2 = 321 – 272 Or, (a – b)2 = 49 Or, a – b = ±7 So desired difference = 7 cm
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