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Which of the following is/are true? I. HCF of p2-p-6 and p6-93 is 1. II. HCF of x+y and x10-y10 is x+y. III. HCF of x+y and x10+y10 is x+y.

Which of the following is/are true? I. HCF of p2-p-6 and p6-93 is 1. II. HCF of x+y and x10-y10 is x+y. III. HCF of x+y and x10+y10 is x+y. Correct Answer Only II

p2-p-6 = (p-3)(p+2) and p6-93 = p6-36 = (p+3)(p-3)(p4+9p+81). Hence, HCF is p-3. We know that x+y and x-y are factors of x10-y10. Therefore, HCF of x+y and x10-y10 is x+y. We know that x+y and x-y are not the factors of x10+y10. Therefore, HCF of x+y and x10+y10 is 1. Therefore, only statement II is true.

Related Questions

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