Prove that x? – 34y? = -1 has no integer solutions. (Hint: First find the minimal positive integer solution of the related equation x? – 34y² = 1, then use this to bound the number of possibilities you have to check for the original equation.)

Q: Show that the equation x+y* : integer. 100 has no solution when each of x and y is a positive

A: To show x4+y4= 100 has no solution when each of x and y is a positive integer.

Q: Which of the following is not a quadratic equation: O(x - 2)² + 1 = 2x - 3 O x(x + 1) +8= (x +…

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Q: What are the solutions to the quadratic equation x2 – 16 = 0? x = 2 and x = –2 x = 4 and x = –4 x =…

A:

Q: · Determine all integer solutions to the following equations such that 0 < x, Y < 150. Show all your…

A: Given 589x+1147y=311  --- Eq 1989x-437y=1150    --- Eq 2From Eq 2:989x=1150+437yx=1150989+437989y…

Q: 7. Solvé the ing equations using the quadratic formula. (Hint: Rewrite each equation so that one…

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Q: Solve the following quadratic equation for all values of x in simplest form. (3x – 1)2 – 49 = –13 -

A: Given : 3x-12-49 = -13

Q: f 2 is one root of the equation 4x3 + kx – 24 = 0, then the value of k is       8   –1…

A: The standard form of a cubic equation is given by ax3+bx2+cx+d=0, where a≠0. If a=0, the cubic…

Q: Solve the equation In (x + 2) + In (x – 1) = In (9x – 17) and check your answers (True / False) %3D

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Q: b. Express each equationin standard form 1. 12y2 – 4x2 – 16x + 72y + 44 = 0 2. x2 – 2y2 + 6x + 4y +…

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Q: A root of the following quadratic equation in x (a # 2): (a − 2)x² + a²x + 4 = 0 is x = -1. What is…

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Q: Which is a solution to (x – 3)(x + 9) = –27?

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Q: Find the value of the real number a if -1 – 2i is a root of the equation z² + az +5 =0. What is the…

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Q: Solve the following quadratic by square rooting. 0 = 3z2 + 18 The solutions are and L. L.

A: Answer

Q: Find all integer solutions to the diophantine equation 64x + 43y = 1.

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Q: Prove that the following equation has no natural solutions x? + x +1 = y².

A: we have to prove that given equation has no natural solution

Q: Show that if u is an odd integer ,then the equation x2 +x−u=0 has no solution that is an integer.

A: The objective is to prove that x2+x-u=0 has no solution that is an integer. Suppose that there…

Q: Find all integer solutions to 66X + 42Y = 258. Also find all solutions (x, y) with x, y positive…

A: Given : 66X + 42Y = 258

Q: Show that the equation 2³ + 3y3 = 923 has no solution in integers, other than x = y = z = 0.

A: Suppose that, x3+3y3=9z2 has a non-trivial solution, that is other than (0,0,0), and minimal.

Q: Prove that there are no integer solutions to the equation x2 = 4y + 3

A: Given equation:- x²=4y+3  We have to prove that the given equation don't satisfy integer pair of x…

Q: What are the roots of the equation x2 – 10x + 26 = 0 in simplest a + bi form?

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Q: Find the real numbers x and y if  2x –i = 6 + ( 1 – y )i

A: Given that  2x –i = 6 + ( 1 – y )i Find the real numbers x and y if

Q: Find all possible pairs of integers x, y so that 7x + 3y = 4. Then find which of these pairs makes…

A: Given:   7x+3y=4                        ........(1) We have to find all possible pairs of integers…

Q: What are the roots of the equation x2 – 2x + 17 = 0 in simplest a + bi form?

A: We know that roots of the quadratic equation ax2+bx+c=0 is given by x=-b±b2-4ac2a Now, the given…