Question
The sum of the total surface areas of two cubes is 1548
cm2. If the product of the length of their edges is 97 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 = 1548 Or, a2 + b2 = 1548/6 = 258 And, ab = 97 Using the formula, x2 + y2 = (x – y)2 + 2xy 258 = (a – b)2 + 2 × 97 Or, (a – b)2 = 258 – 194 Or, (a – b)2 = 64 Or, a – b = ±8 So desired difference = 8 cm
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