sin(arcsin(5x^2))=6-x ПОМОГИТЕ РЕШИТЬ. Created by 58shybook. algebra-ru

sin(arcsin(5x^2))=6-x ПОМОГИТЕ РЕШИТЬ...

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$\boxed {\; sin(arcsinx)=x\; ,\; \; esli\; \; -1\leq x\leq 1\; }\\\\\\sin(arcsin5x^2)=6-x\; \; ,\; \; -1\leq 5x^2\leq 1\; \; \; \Rightarrow \\\\-\frac{1}{5}\leq x^2\leq \frac{1}{5}\; \; ,\; \; 0\leq x^2\leq \frac{1}{5}\; \; ,\; \; x^2-\frac{1}{5}\leq 0\; \; ,\; \; (x-\frac{1}{\sqrt5})(x+\frac{1}{\sqrt5})\leq 0\; ,\\\\x\in [-\frac{1}{\sqrt5}\, ;\, \frac{1}{\sqrt5}\; ]\qquad \frac{1}{\sqrt5}\approx 0,45\\\\\\5x^2=6-x\; \; ,\; \; \; 5x^2+x-6=0\; \; ,\; \; D=121\; ,\\\\x_1=-1,20,45$

$Otvet:\; \; x\in \varnothing \; .$

1 votes Thanks 1

dimonignatov00

Ответ:не имеет решения

Объяснение:

Sin(arcsin5x^2)=6-x

По формуле: Sin(arcsinx)=x.

5x^2=6-x

5x^2+x-6=0

Решаем через дискриминант

D=1+120=121; √121=11

X1=1; x2= -6/5

0 votes Thanks 1

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