Question 4.
For natural numbers x,y, and z, if xy + yz = 19 and yz + xz = 51, then the minimum possible value of xyz is
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Question Explanation
Text ExplanationVideo Explanation
xy + yz = 19
y(x + z) = 19
Observe that 19 is prime and can’t be factorized further. Since x, y and z are all natural
numbers, the value of (x + z) can’t be 1. (It should at least be 2).
Therefore, y = 1 and ( x + z) = 19
yz + xz = 51
z(y + x) = 51
z(x + 1) = 51
51 = 17 * 3
Case 1: z = 17, x + 1 = 3
x = 2, y = 1, z = 17
xyz = 2 * 1 * 17 = 34
Case 2: z = 3, x + 1 = 17
x = 16, y = 1, z = 3
xyz = 16 * 1 * 3 = 48
Hence the minimum value of x * y * z = 34
Hence, the answer is '34'
