\(2^{100}\) và \(10^{31}\)

taco \(2^{100}=\left(2^{69}\right)^{31}\)

=>\(2^{100}< 10^{31}\)

\(=(3x-11)(2x-1)(2x+1)-(9x-3)(2x-1)(2x-1)\)

\(=(2x-1)[(3x-11)(2x+1)-(9x-3)(2x-1)]\)

\(=(2x-1)[6x^2-10x-11-(18x^2-4x+3)]\)

\(=-(2x-1)(12x^2+6x+14)\)

b)\(=-2(x^2-1/2x-5/2) =-2(x^2-2x.1/4+1/16-41/16)\)

\(\text{=-2(x-1/4)^2+41/8}\)

\(Vi -2(x-1/4)^2≤0=>-2(x-1/4)^2+41/8≤41/8∀x\)

=> GTLN cua B\(=41/8 <=>x=1/4\)

\(A=x^2-3x-5\)

\( =x^2-2.1,5x+2,25-7,25\)

\(=(x-1,5)^2-7,25\)

\(Vi (x-1,5)^2≥0 ∀x=>(x-1,5)^2-7,25≥-7,25\)

=> GTNN của A=\(-7,25<=> x=1,5\)

b) 

\(3(x-1)^2-(1-x)^2+2(x-3)(x+3)-(2x+3)^2-(5-16x)\)

\(=3(x^2-2x+1)-(1-2x+x^2)+2(x^2-9)-(4x^2+12x+9)-5+16x\)

=-30

=>PT ko phu thuoc vao bien x