Question

Prove that all the solutions to the equation x^{2} = 4x
-3 are rational. Justify your answers.

(subject is computer theory)

Answer #1

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Find all solutions of the equation. (Enter all answers including
repetitions. Enter your answers as a comma-separated list.)
x4 + 5x3− 17x2− 15x
+ 42 = 0
Find all solutions of the equation. (Enter
all
answers including repetitions. Enter your
answers as a comma-separated list.)
6x5 + 43x4 + 37x3 − 30x2 = 0
Find all solutions of the equation. (Enter
all answers including repetitions. Enter your answers as a
comma-separated list.)
x3 − 8x2 − 19x − 10...

Prove that f(x) = (10x3 + 25x + 63) / (4x – 3) is O(x2) directly
from the definition of big O. In lecture we did a big O proof for a
similar rational function. To do your proof, bound the numerator
from above by a simple function on x3 and bound the denominator
from below by a simple function on x. That will allow you do bound
f by a simple function on x2 . If you do your...

Verify that the equation does not have any rational number
solutions.
x4 − x3 − 8x2 − 2x + 1 = 0
Find all possible rational roots. (Enter your answers as a
comma-separated list.)

1. Solve. (Find all complex-number solutions.)
x2 + 4x + 6 = 0
2. Solve by factoring:
x2 + 5x = −6
PLEASE SOLVE BOTH & WRITE STEPS IN DETAIL ON YOU SOLVED
IT!

Prove that following equations have no rational solutions.
a) x^3 + x^2 = 1
b) x^3 + x + 1 = 0
d) x^5 + x^4 + x^3 + x^2 + 1 = 0

Use the Rational Root Theorem to find all roots of f(x) = 4x 3 −
3x + 1.

Find all solutions in positive integers of the Diophantine
equation x2 + 3y2 = z2

A graphing calculator is recommended. Use Newton's method to
find all solutions of the equation correct to eight decimal places.
Start by drawing a graph to find initial approximations. (Enter
your answers as a comma-separated list.) -2x^7-4x^4+9x^3+2=0

consider the following function f(x)=x2-3x/x2-4x+3
find all x inter and the equations of all vertical
asymptotes

Solve the equation by completing the square. (Enter your answers
as a comma-separated list.)
x2 = −4x − 53
Solve the quadratic inequality. (Enter your answer using
interval notation. If there is no solution, enter NO SOLUTION.)
x2 − 8x > −12
Solve the equation by factoring. (Enter your answers as a
comma-separated list.)
125x = 5x3

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