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13 votes
X³ + 6x -7= 0 là phương trình

User KodingKid
by
6.1k points

2 Answers

2 votes

Answer:(x-1) *(x^2 + x + 7)

Explanation:

1. rewrite

2. factor the expression

User Lviggiani
by
6.2k points
5 votes

Answer:


\huge\boxed{\bf\:x = 1}

Explanation:


x ^ { 3 } +6x-7=0

By using the rational root theorem, all rational roots of a polynomial are in the form p/q, where p divides the constant term -7 & q divides the leading coefficient, 1. Now, let's list out all the possible candidates for p/q by following this theorem.


(+/-)7, (+/-)1

Now, let's substitute the value of x as these integers. By using the trial & error method, we can see that..


x = 1

This means that 1 factor of the above equation will be:


x = 1\\\Longrightarrow\:x - 1 = 0

So, by using the Factor theorem, we know that, x - k will be the factor of the polynomial for each root k. Now, divide x³ + 6x - 7 by x - 1. We'll the value as:


(x^(3) + 6x - 7)/(x - 1)\\\Longrightarrow \: x^(2)+x+7=0

We now have a quadratic equation with us. By using the biquadratic formula: -b ± √b² - 4ac / 2a, where,

  • a = 1
  • b = 1
  • c = 7

So,


x=\frac{-1(+/-)\sqrt{1^(2)-4* 1* 7}}{2} \\x=(-1(+/-)√(-27))/(2)

Here, we can see that,


x\in \emptyset

Then, by listing out the solutions that we found, the value of x will be:


\boxed{\bf\:x = 1}


\rule{150}{2}

User Jstanley
by
7.0k points
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