Question

(х²-6х)²+(х²-6х)-30=0

Answer 1

Решение на прикреплённой фотографии

Answer 2

To solve the quadratic equation $(x^2 - 6x)^2 + (x^2 - 6x) - 30 = 0$, you can use substitution to simplify the equation. Let's make a substitution:

Let $y = x^2 - 6x$, so the equation becomes:

$y^2 + y - 30 = 0$

Now, you have a quadratic equation in terms of $y$. To solve this quadratic equation, you can factor it:

$(y + 6)(y - 5) = 0$

Now, set each factor equal to zero and solve for $y$:

1. $y + 6 = 0$: $y = -6$

2. $y - 5 = 0$: $y = 5$

Now that you have two possible values for $y$, you need to back-substitute them into the expression for $y$ in terms of $x$:

For $y = -6$: $x^2 - 6x = -6$

For $y = 5$: $x^2 - 6x = 5$

Now, solve these two equations for $x$:

1. $x^2 - 6x = -6$: Add 6 to both sides: $x^2 - 6x + 6 = 0$

   You can solve this quadratic equation using the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

   Here, $a = 1$, $b = -6$, and $c = 6$. $x = \frac{6 \pm \sqrt{(-6)^2 - 4(1)(6)}}{2(1)}$

   $x = \frac{6 \pm \sqrt{36 - 24}}{2}$

   $x = \frac{6 \pm \sqrt{12}}{2}$

   $x = \frac{6 \pm 2\sqrt{3}}{2}$

   $x = 3 \pm \sqrt{3}$

2. $x^2 - 6x = 5$: Subtract 5 from both sides: $x^2 - 6x - 5 = 0$

   You can again solve this quadratic equation using the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

   Here, $a = 1$, $b = -6$, and $c = -5$. $x = \frac{6 \pm \sqrt{(-6)^2 - 4(1)(-5)}}{2(1)}$

   $x = \frac{6 \pm \sqrt{36 + 20}}{2}$

   $x = \frac{6 \pm \sqrt{56}}{2}$