Prove that x^n-Y^n divisible by x-y for all natural numbers x,y (x!=y),and n.

Answers

Answer 1

Answer: Let's do that by induction :
For $n=1$ , $x^1-y^1$ is obviously divisible by $x-y$

If we assume the property holds at rank $n$ , then $x^(n+1)-y^(n+1)=x(x^n-y^n)+y^n(x-y)$ . Since $x^n-y^n$ is divisible by $(x-y)$ , we have $A$ such that $x^n-y^n=A(x-y)$ hence $x^(n+1)-y^(n+1)=(x-y)(Ax+y^n)$ .

Hence by induction for all $n\ge1$ , $x-y$ divides $x^n-y^n$

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Solve the equation the square root of the quantity x plus 3 plus 4 equals 5 for the variable.

Answers

Domain: expression under square root is greater or equal than zero.

x+3>0
x>-3

Then:

$√(x+3)}+4=5 \qquad |-4 \n \n √(x+3)=1 \qquad |(...)^2 \n \n x+3=1 \n \n x=-2 \in D$

So the answer is x=-2

Final answer:

By isolating the square root, squaring both sides to remove the square root, and then solving for x, the solution to the equation √(x + 3) + 4 = 5 is found to be x = -2.

Explanation:

To solve this equation, we start by isolating the square root. The equation given is √(x + 3) + 4 = 5. The first step is to subtract 4 from both sides of the equation to isolate the square root, resulting in √(x + 3) = 1.

Once the square root is isolated, we can square both sides of the equation to eliminate the square root, leading to x + 3 = 1² = 1.

Finally, subtract 3 from both sides, leaving us with the solution x = 1 - 3 = -2.

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What is the answer
-8 + 3 + -8 – -3

Answers

-8+3+-8--3
minusing a negativ means adding a positive
adding a negaative means minusing a positive
-8+3-8+3
-5-8+3
-13+3
-10

The Answer would be -10

Make h the subject of the formula

Answers

Answer:

Step-by-step explanation:

what formula????????

Hi could you help me? solve 8-7x=22

Answers

8-7x=22
8-22=7x
7x=8-22
7x=-14
x=-14/7
x=-2

taking 8 to the right hand side,
-7x=22-8
x=14/(-7)
x=-2

What is 7% tax on a $9.79 purchase

Answers

all u do is put 9.79 multiplied by .07 and it gives you 0.6853 so its .68 or .69 cents if u round

all you do is to put 9.79 multiplied by .07 and it gives you 0.6853 so its .68 or .69 cents if u round the decimal

What is 2 1/50 expressed as a decimal

Answers

To make 2 1/50 as a decimal you must first make it improper;

2 1/50 = 101/50

so now to get the decimal just divide the numerator by the denominator;

101 ÷ 50 = 2.02

so 2 1/50 expressed as a decimal is; 2.02

2 1/50 = 2 2/100

2.02 is the answer.

Final answer: 2.02

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