Question

so sánh các biểu thức sau

a) A= 26^2 - 24^2

B= 27^2 -25^2

b) C= (4+1)(4^2+1)(4^4+1)(a^8+1)(4^16+1)

D= 4^32 +1

Answer 1

a)26²-24²=(26-24)(26+24)=2.50=100

27²-25²=(27-25)(27+25)=2.52=104

mà 100<104 => 26²-24²<27²-25²

Answer 2

\(hdt:\left(a-b\right)\left(a+b\right)=a^2-b^2\)

\(3C=3\left(4+1\right)\left(4^2+1\right)\left(4^4+1\right)\left(4^8+1\right)\left(4^{16}+1\right)\)

\(3C=\left(4-1\right)\left(4+1\right)\left(4^2+1\right)\left(4^4+1\right)\left(4^8+1\right)\left(4^{16}+1\right)\)

\(3C=\left(4^2-1\right)\left(4^2+1\right)\left(4^4+1\right)\left(4^8+1\right)\left(4^{16}+1\right)\)

\(3C=\left(4^4-1\right)\left(4^4+1\right)\left(4^8+1\right)\left(4^{16}+1\right)\)

\(3C=\left(4^8-1\right)\left(4^8+1\right)\left(4^{16}+1\right)\)

\(3C=\left(4^{16}-1\right)\left(4^{16}+1\right)=4^{32}-1\Rightarrow3C< D\Rightarrow C< D\)