Question

Срочно!!! 1)Найдите корень уравнения:√30-x=x 2)Найдите корень уравнения:log0.5(8-x)=-5 3)Найдите корень уравнения:9^2+5x=1.8*5^2+5x

Answer 1

1) $\sqrt{30} - x=x \\ 2x= \sqrt{30} \\ x= \frac{ \sqrt{30} }{2} \\ x= \sqrt{ \frac{15}{2} }$
или
$\sqrt{30-x} =x$/ возведем во 2 степень
30-x=x²
все перенесем в одну сторону:
x²+x-30=0
$x_{1} = \frac{-1+ \sqrt{1+120} }{2}= \frac{-1+11}{2} = 5 \\ x_{2} = \frac{-1- \sqrt{1+120} }{2}= \frac{-1-11}{2} =-6$
2) $log_{0,5}(8-x)=-5$
8-x=$(\frac{1}{2} )^{-5}$             ОДЗ
8-х=2⁵                                                    8-х>0
8-x=32                                                    x<8
x=8-32
x=-24
Ответ: -24
3) 
9^(2+5x)=1,8*5^(2+5x)
9^2*9^(5x)=1,8*5^2*5^(5x)
9^(5x)/5^(5x)=(1,8*25)/81
(9/5)^(5x)=(0,2*25)/9
(9/5)^(5x)=5/9
(5/9)^(-5x)=5/9
-5x=1
x=-1/5
x=-0,2
Ответ: х=-0,2

Answer 2

I can help you with solving these equations. Here are the detailed steps and answers:

1) To find the root of the equation $$\sqrt{30-x}=x$$, we need to square both sides and simplify. We get $$30-x=x^2$$ or $$x^2+x-30=0$$. This is a quadratic equation that can be solved by factoring or using the quadratic formula. By factoring, we get $$(x+6)(x-5)=0$$. Therefore, the possible roots are $$x=-6$$ or $$x=5$$. However, we need to check if these roots satisfy the original equation, because squaring both sides may introduce extraneous roots. Plugging in $$x=-6$$, we get $$\sqrt{30-(-6)}=-6$$ or $$\sqrt{36}=-6$$, which is false. So $$x=-6$$ is an extraneous root. Plugging in $$x=5$$, we get $$\sqrt{30-5}=5$$ or $$\sqrt{25}=5$$, which is true. So $$x=5$$ is the only root of the equation.

2) To find the root of the equation $$\log_{0.5}(8-x)=-5$$, we need to rewrite the logarithm in exponential form. We get $$8-x=0.5^{-5}$$ or $$8-x=32$$. Solving for $$x$$, we get $$x=8-32$$ or $$x=-24$$. This is the root of the equation.

3) To find the root of the equation $$9^2+5x=1.8*5^2+5x$$, we need to simplify and isolate $$x$$. We get $$81+5x=50+5x$$ or $$81-50=5x-5x$$. Simplifying further, we get $$31=0$$. This is a contradiction, which means that the equation has no solution. There is no root for this equation.