1963 AHSME Problems/Problem 40
Problem
If is a number satisfying the equation , then is between:
Solution 1
Let and . Cubing these equations, we get and , so . The left-hand side factors as
However, from the given equation , we get . Then , so .
Squaring the equation , we get . Subtracting this equation from the equation , we get , so . But and , so , so . Cubing both sides, we get , so . The answer is .
Solution 2
i.e,
if the sum of three numbers is zero, then their sum of cubes is thrice the product of each number. then, . by solving this, we get . this gives the step what we had done in solution 1.The answer is .
Solution 3
Cubing both sides to get rid of the messy cube roots, we get so Dividing both sides by 3 and cubing, we find , which is between .
See Also
1963 AHSC (Problems • Answer Key • Resources) | ||
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