Question

Решите уравнение методом замены переменной (x^2-8)-^2 -5(x^2-8)-14+=0 (x+7)^4 -17(x+7)^2 +16=0

Answer 1

Ты правильно пример написала? а то приходится миллионами ворочить

Answer 2

I can help you with solving equations using the method of substitution. Here is a detailed solution for your equation.

First, let's rewrite the equation as $$\left(x^2-8\right)^2-5\left(x^2-8\right)-14=0$$ Now, let's introduce a new variable $$y=x^2-8$$ and substitute it in the equation. We get $$y^2-5y-14=0$$ This is a quadratic equation that can be solved by factoring or using the quadratic formula. The factors of $$y^2-5y-14$$ are $$(y-7)(y+2)$$, so we can write $$y^2-5y-14=(y-7)(y+2)=0$$ To find the values of $$y$$ that satisfy the equation, we set each factor equal to zero and solve for $$y$$. $$y-7=0 \implies y=7$$ $$y+2=0 \implies y=-2$$ Now, we have two possible values for $$y$$, but we need to find the values of $$x$$ that correspond to them. To do that, we use the original substitution $$y=x^2-8$$ and plug in the values of $$y$$ one by one. For $$y=7$$, we get $$7=x^2-8 \implies x^2=15 \implies x=\pm\sqrt{15}$$ For $$y=-2$$, we get $$-2=x^2-8 \implies x^2=6 \implies x=\pm\sqrt{6}$$ Therefore, the equation has four solutions: $$x=\sqrt{15}, -\sqrt{15}, \sqrt{6}, -\sqrt{6}$$

I hope this helps you understand how to solve equations using the method of substitution. If you have any other questions, feel free to ask me.Решите уравнение методом замены переменной (x^2-8)-^2 -5(x^2-8)-14 =0 (x+7)^4 -17(x+7)^2 +16=0