Tell the three no.s that if you add or multiple the answer is 6.
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As the other answerers have said, 1, 2, and 3 are three such numbers. To find all such triplets, note that if x, y, and z are three such numbers whose sum is 6 and whose product is 6, then:
x + y + z = 6 and xyz = 6.
Notice that this is a system of 2 equations in 3 unknowns, so there are infinitely many solutions. We can let one of the variables be any value and solve the resulting system to find the other two. For example, if x = 1, then the system becomes:
1 + y + z = 6 and (1)yz = 6 ==> y + z = 5 and yz = 6,
which has solutions (x, y, z) = (1, 2, 3) and (1, 3, 2), giving 1, 2, and 3 as three such numbers. You can let x be anything and then solve the resulting system for y and z to find another triplet of numbers.
I hope this helps!
x + y + z = 6 and xyz = 6.
Notice that this is a system of 2 equations in 3 unknowns, so there are infinitely many solutions. We can let one of the variables be any value and solve the resulting system to find the other two. For example, if x = 1, then the system becomes:
1 + y + z = 6 and (1)yz = 6 ==> y + z = 5 and yz = 6,
which has solutions (x, y, z) = (1, 2, 3) and (1, 3, 2), giving 1, 2, and 3 as three such numbers. You can let x be anything and then solve the resulting system for y and z to find another triplet of numbers.
I hope this helps!
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