Question

Các bạn làm giúp mình mấy bài này mai mình phải nộp rồi

Answer 1

Bài 1:

Nếu $a+b+c=0$ thì đkđb thỏa mãn

$M=\frac{(-c)(-a)(-b)}{abc}=\frac{-(abc)}{abc}=-1$

Nếu $a+b+c\neq 0$. Áp dụng TCDTSBN:

$\frac{a+b-c}{c}=\frac{a+c-b}{b}=\frac{b+c-a}{a}=\frac{a+b-c+a+c-b+b+c-a}{c+b+a}=\frac{a+b+c}{a+b+c}=1$

$\Rightarrow a+b-c=c; a+c-b=b; b+c-a=a$

$\Leftrightarrow a+b=2c; a+c=2b; b+c=2a$

$\Rightarrow a=b=c$

$M=\frac{(a+a)(a+a)(a+a)}{aaa}=\frac{8a^3}{a^3}=8$

Answer 2

Bài 2a

Đặt $2x=3y=4z=t$

$\Rightarrow x=\frac{t}{2}; y=\frac{t}{3}; z=\frac{t}{4}$

Khi đó:

$|x+y+3z|=1$

$\Leftrightarrow |\frac{t}{2}+\frac{t}{3}+\frac{3t}{4}|=1$

$\Leftrightarrow |\frac{19}{12}t|=1$

$\Rightarrow t=\pm \frac{12}{19}$

Nếu $t=\frac{12}{19}$ thì:

$x=\frac{t}{2}=\frac{6}{19}; y=\frac{4}{19}; z=\frac{3}{19}$

Nếu $t=-\frac{12}{19}$ thì:

$x=\frac{t}{2}=\frac{-6}{19}; y=\frac{-4}{19}; z=\frac{-3}{19}$

Answer 3

Bài 2b:

$\frac{x^3}{8}=\frac{y^3}{27}=\frac{z^3}{64}$

$\Leftrightarrow (\frac{x}{2})^3=(\frac{y}{3})^3=(\frac{z}{4})^3$

$\Leftrightarrow \frac{x}{2}=\frac{y}{3}=\frac{z}{4}$

Đặt $\frac{x}{2}=\frac{y}{3}=\frac{z}{4}=t$

$\Rightarrow x=2t; y=3t; z=4t$

Khi đó:
$x^2+2y^2-3z^2=-650$

$\Leftrightarrow (2t)^2+2.(3t)^2-3(4t)^2=-650$

$\Leftrightarrow -26t^2=-650$

$\Leftrightarrow t=\pm 5$

Nếu $t=5$ thì:

$x=2t=10; y=3t=15; z=4t=20$

Nếu $t=-5$ thì:

$x=2t=-10; y=3t=-15; z=4t=-20$

Answer 4

Bài 3:

Nếu $x\geq 5$ thì:

$|x^2-9|+|x^2-25|=26$

$\Rightarrow x^2-9+x^2-25=26$

$\Leftrightarrow 2x^2=60$

$\Leftrightarrow x^2=30$

$\Rightarrow x=\sqrt{30}$ (thỏa mãn)

Nếu $3\leq x< 5$ thì:

$|x^2-9|+|x^2-25|=26$

$\Leftrightarrow x^2-9+25-x^2=26$

$\Leftrightarrow 16=26$ (vô lý)

Nếu $-3\leq x< 3$ thì:

$|x^2-9|+|x^2-25|=26$

$\Leftrightarrow 9-x^2+25-x^2=26$

$\Leftrightarrow x^2=4\Rightarrow x=\pm 2$ (tm)

Nếu $-5\leq x< -3$ thì:

$|x^2-9|+|x^2-25|=26$

$\Leftrightarrow x^2-9+25-x^2=26$

$\Leftrightarrow 16=26$ (vô lý)

Nếu $x< -5$ thì:

$|x^2-9|+|x^2-25|=26$

$\Leftrightarrow x^2-9+x^2-25=26$

$\Leftrightarrow x=-\sqrt{30}$

Answer 5

Bài 4: Đề lỗi.