Bài 8:

a) \(2^{225}=\left(2^3\right)^{75}=8^{75}\)

\(3^{150}=\left(3^2\right)^{75}=9^{75}\)

Vì \(8^{75}< 9^{75}\Rightarrow2^{225}< 3^{150}\)

b) \(2^{91}=\left(2^{13}\right)^7=8192^7\)

\(5^{35}=\left(5^5\right)^7=3125^7\)

Vì \(8192^7>3125^7\Rightarrow2^{91}>5^{35}\)

c) \(99^{20}=\left(99^2\right)^{10}=9801^{10}< 9999^{10}\)

7520 = 4510.530

Ta có: 4510.530 = (9.5)10.530 = 910.510.530 = (32)10.540

=320.(52)20 = 320.2520 = (3.25)20 = 7520

Vế phải bằng vế trái nên đẳng thức được chứng minh

um

đẳng thức đâu?

\(\dfrac{x^2+2x+1}{2x^2+x-1}=\dfrac{\left(x+1\right)^2}{\left(x+1\right)\left(2x-1\right)}\)

=(x+1)/(2x-1)

Đề ạ

\(sin^6a+cos^6a=\left(sin^2a\right)^3+\left(cos^2a\right)^3\)

\(=\left(sin^2a+cos^2a\right)^3-3sin^2a.cos^2a\left(sin^2a+cos^2a\right)\)

\(=1-3sin^2a.cos^2a\)

d, \(\dfrac{\left(sinx+cosx\right)^2-1}{2cotx-sin2x}=tan^2x\)

\(\Leftrightarrow\dfrac{sin^2x+cos^2x+2sinx.cosx-1}{2cotx-sin2x}=tan^2x\)

\(\Leftrightarrow2sinx.cosx=tan^2x\left(2cotx-sin2x\right)\)

\(\Leftrightarrow2sinx.cosx=\dfrac{sin^2x}{cos^2x}\left(2\dfrac{cosx}{sinx}-2sinx.cosx\right)\)

\(\Leftrightarrow sinx.cosx=\dfrac{sinx}{cosx}-\dfrac{sin^3x}{cosx}\)

\(\Leftrightarrow sinx.cos^2x=sinx-sin^3x\)

\(\Leftrightarrow sinx.cos^2x=sinx\left(1-sin^2x\right)\)

\(\Leftrightarrow sinx.cos^2x=sinx.cos^2x\)

\(\Rightarrowđpcm\)

a, \(\left(1-sin^2x\right).tan^2x+\left(1-cos^2x\right).cot^2x=1\)

\(\Leftrightarrow cos^2x.\dfrac{sin^2x}{cos^2x}+sin^2x.\dfrac{cos^2x}{sin^2x}=1\)

\(\Leftrightarrow sin^2x+cos^2x=1\)

\(\Rightarrowđpcm\)

b, \(1-sin^2x-sin^2x.cot^2x=0\)

\(\Leftrightarrow cos^2x-cos^2x=0\)

\(\Rightarrowđpcm\)

c, \(cos^4x+sin^2x.cos^2x+sin^2x=1\)

\(\Leftrightarrow\left(cos^2x+sin^2x\right).cos^2x+sin^2x=1\)

\(\Leftrightarrow cos^2x+sin^2x=1\)

\(\Rightarrowđpcm\)