Use mathematical Inductlon to prove that for r>0 and any positive Integer

Q: Prove that (-1+ iE)" + (-1- i5" has either the velue 2n+! or the value -2" f ロ ww. š any integer…

A: The cube root of unity is written as:

Q: Suppose x is a real number. Prove that if x 2, then there is a real number y such that x =…

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Q: Let p, q, and r be real numbers such that p + q +r = 26 and '/p + lq + '/, = 31. What is the value…

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Q: Recall the property that (a, b) = 1 if and only if ax + by = 1 for some integer x, y. Use this…

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Q: theorem Every Ving Can be imbeobling în aving with

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Q: If A = {r|- 23 < x < 3how many negative integers does Acontain? Note that: 'I' means 'Such that'

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Q: Prove that: cscz- cot z = 1 2. 2. %3D

A: We need to prove the identity  csc2z-cot2z=1

Q: (4b) Prove that there exists no positive integer x such that 2x < x² < 3x.

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Q: Let x, y be real numbers such that xy=1x and x≠y. Prove that x^2+y^2≥2\sqrt{2}|x−y|.

A: Given: xy=1x,x≠y To find: x2+y2≥22x-y

Q: Prove that 1 + nx is less than or equal to (1+x)^n for all real numbers x>-1 and integers n >=2…

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Q: Show that the identity k n = n 72 n k k-1, olds for all integers 1 <k<n and use it to prove that n…

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Q: Let n be an odd integer, a > 0, and b < 0. Prove that x" + ax + b= 0 has a unique root. Hint: If…

A: Let n be an odd integer, a &gt; 0, and b &lt; 0. Prove that xn + ax + b = 0 has a unique root

Q: State the Fermet's Last Theorem. Who was French women mathematican who mede significant 19th century…

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Q: Prove that there is a positive number z so that z^5 + 10z = 10.

A: TO PROVE:-  There is a positive number z satisfying z5+10z=10 GIVEN :- z5+10z=10

Q: Rind the Domain Jx-3 x2 16

A: Given query is to find the attached domain of the expression.

Q: Use direct prove to prove that for any two positive numbers x and y, x+y Vxy s 2

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Q: If x and y are real numbers and x>1, prove that there exists a positive integer n such that xn > y

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Q: Show and use d(Xn, FCN))<« d(Xn-1 'x) Vny? To prove X = fx) %3D

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Q: Draw a graph of a function, f(x), in the first quadrant, and shade an area under the curve along a…

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Q: 5x+h over 5x+h+3 minus 5x over 5x+3, all over h. This is a difference quotient problem in…

A: LCD of the numerator is (5x+5h+3)(5x+3).We make both denominators same then subtract the rational…

Q: ve that if x5 – 3x4 + 2x

A: Introduction: In an equation, the two expressions are assumed to be equal, as indicated by the…

Q: Prove or disprove that ⌈x + y⌉ = ⌈x⌉ + ⌈y⌉ for all real numbers x and y.

A: According to the given information, It is required to prove or disprove that:

Q: Solve the following autonomous differential equation with the given initial condition. dy = - 0.4y,…

A: The answer and the detailed explanation is given below-

Q: Suppose the following theorem is proven using a direct proof. Theorem: If x is a real number and x…

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Q: Show dz 4 In= 는I미페 - for a<0. x <

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Q: How many bijective functions have [10] as both the domain and codomain

A: Given, 10

Q: Suppose that m andn are positive integers and b is a real number so that the principal n" root of b…

A: We have been given that nth root of b exists where b is the real number.

Q: Show that the polynomial 1+x+x² +... +xP-1 , where p is a prime number, is irreducible over the…

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