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Aleonysh [2.5K]
3 years ago
13

Find three consecutive odd numbers the product of which is 148 more than the cube of their middle number.

Mathematics
1 answer:
Anna11 [10]3 years ago
3 0

Answer:

   The numbers are -39,-37,-35

Step-by-step explanation:

Let

x-----> the first odd number

x+2----> the middle odd number

x+4---> the third odd number

x(x+2)(x+4)=(x+2)^{3} +148

(x^{2}+2x)(x+4)=(x^{2}+4x+4)(x+2)+148\\x^{3}+4x^{2}+2x^{2}+8x=x^{3}+2x^{2}+4x^{2}+8x+4x+8+148\\x^{3}+6x^{2}+8x=x^{3}+6x^{2}+12x+156\\8x=12x+156\\4x=-156\\x=-39

The numbers are

x=-39

x+2=-39+2=-37

x+4=-39+4=-35

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