Question
The sum of the total surface areas of two cubes is 1572
cm2. If the product of the length of their edges is 99 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 = 1572 Or, a2 + b2 = 1572/6 = 262 And, ab = 99 Using the formula, x2 + y2 = (x – y)2 + 2xy 262 = (a – b)2 + 2 × 99 Or, (a – b)2 = 262 – 198 Or, (a – b)2 = 64 Or, a – b = ±8 So desired difference = 8 cm
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