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Sergio039 [100]
3 years ago
14

The sum of a number and six times its reciprocal is 10. Find the number​

Mathematics
1 answer:
Andreas93 [3]3 years ago
6 0

Answer:

two solutions work: x = 5 + \sqrt{19} and x = 5 - \sqrt{19}

Step-by-step explanation:

x + 6 ( 1/x ) = 10

x^2 + 6 = 10x

x^2 - 10x + 6 = 0

x = 5 + \sqrt{19}, 5 - \sqrt{19}

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Answer:

Consider f: N → N defined by f(0)=0 and f(n)=n-1 for all n>0.

Step-by-step explanation:

First we will prove that f is surjective. Let y∈N be any natural number. Define x as the number x=y+1. Then x∈N, and f(x)=x-1=(y+1)-1=y.  We conclude that f is surjective.

However, f is not injective. Take x1=0 and x2=1. Then x1≠x2 but f(x1)=0 and f(x2)=x2-1=1-1=0. We have shown that there are two natural numbers x1,x2 such that x1≠x2 but f(x1)=f(x2), that is, f is not injective.

Note:

If 0∉N in your definition of natural numbers, the same reasoning works with the function f: N → N defined by f(1)=1 and f(n)=n-1 for all n>1. The only difference is that you consider x1=1, x2=2 for the injectivity.

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3 years ago
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Answer : option A

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