The difference of two perfect cubes is 386. If the cube root of the smaller of the two numbers is 7, then the cube root of the l
arger number is
1 answer:
Answer:
9
Step-by-step explanation:
Let the two perfect cubes be x and y where x > y.
According to the given conditions:
![{x}^{3} - {y}^{3} = 386...(1) \\ y = 7...(2) \\ plug \: y = 7 \: in \: equation \: (1) \\ {x}^{3} - {7}^{3} = 386 \\ {x}^{3} - 343 = 386 \\ {x}^{3} = 343 + 386 \\ {x}^{3} = 343 + 386 \\ {x}^{3} = 729 \\ x = \sqrt[3]{729} \\ x = 9](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B3%7D%20%20-%20%20%7By%7D%5E%7B3%7D%20%20%3D%20386...%281%29%20%5C%5C%20y%20%3D%207...%282%29%20%5C%5C%20plug%20%5C%3A%20y%20%3D%207%20%5C%3A%20in%20%5C%3A%20equation%20%5C%3A%20%281%29%20%5C%5C%20%20%7Bx%7D%5E%7B3%7D%20%20-%20%20%7B7%7D%5E%7B3%7D%20%20%3D%20386%20%5C%5C%20%7Bx%7D%5E%7B3%7D%20%20-%20%20343%20%3D%20386%20%5C%5C%20%7Bx%7D%5E%7B3%7D%20%20%20%20%20%3D%20343%20%20%2B%20%20386%20%5C%5C%20%7Bx%7D%5E%7B3%7D%20%20%20%20%20%3D%20343%20%20%2B%20%20386%20%5C%5C%20%7Bx%7D%5E%7B3%7D%20%20%20%3D%20729%20%5C%5C%20x%20%3D%20%20%5Csqrt%5B3%5D%7B729%7D%20%20%5C%5C%20x%20%3D%209)
Thus the cube root of the larger number is 9.
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