Which of the following equations has the solution \( x= \) all real numbers? \( 4(3-x)+6 x=3 x+12+2 x \) \( 4(3-x)+6 x=3 x+10-x \) \( 4(3-x)+6 x=x+12-3 x \) \( 4(3-x)+6 x=3 x+12-x \)

3. Résoudre les équations suivantes: (a) \( \log _{x}(x-2)=\log _{x-2}(x) \)

Diberikan polinomial \( P(x)=x^{3}-5 x^{2}+4 x+4 \) \( Q(x)=-x^{2}-7 x+9 \) Nilai dari \( P(x)-Q(x)=\cdots \) A. \( \quad x^{3}-6 x^{2}-3 x+13 \) B. \( x^{3}-6 x^{2}-2 x+13 \) C. \( x^{3}+6 x^{2}-3 x+13 \) D. \( x^{3}+6 x^{2}-2 x+13 \) E. \( \quad x^{3}+6 x^{2}+3 x+13 \)

\( a^{2}=4 a+4 \) \( b^{2}=4 b+4 \) olduğuna göre, \( \frac{a-4}{a^{2}}+\frac{4}{b^{2}} \) kaçtır?

10. \( g(t)=\left(t+\frac{1}{t}\right)\left(5 t^{2}-\frac{1}{t^{2}}\right) \)

10. a. Show that the roots of the equation \( 2\left(a^{2}+b^{2}\right) x^{2}+2(a+b) x+1=0 \) can never be real unless \( a=b \). b. Prove that the roots of the equation \( x^{2}+(2 k-1) x+k^{2}=0 \) are real roots if \( k \leq \frac{1}{4} \).