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 \( k \leq \frac{1}{4} \).

Сложите почленно неравенства. \( 11<13 \) и \( 5,1>2,7 \)

Analizar y graficar 3) \( y=2 x^{2}-4 x+5 \)

a) \( \left(3^{6}\right)^{7} \cdot 3^{2}: 3^{41}-5^{2}= \) c) \( \left[\left(2^{2}\right)^{3}\right]^{3}:\left(2^{3}\right)^{5}= \) e) \( 4^{3} \cdot\left(4^{5}\right)^{4}:\left(4^{3}\right)^{7}-2^{4}= \) g) \( \left[\left(5^{3}\right)^{12}:\left(5^{2}\right)^{17}-25\right]: 5= \) i) \( \left.2^{6}+10 \cdot\left[3 \cdot 3^{3}-\left(3^{4}\right)^{3}: 3^{11}\right)\right]= \)

d) \( \frac{3^{4}: 3}{3^{2}}= \)

If \( 33-a=a+27-5 a \), what is the value of \( 33+3 a ? \)