\(A=\frac{15^8-1+3}{15^8-1}=1+\frac{3}{15^8-1}\)

\(B=\frac{15^8-3+3}{15^8-3}=1+\frac{3}{15^8-3}\)

Ta có: \(15^8-3< 15^8-1\)

=> B>A

1)  \(A^2=2+2.\frac{\sqrt{\left(8+\sqrt{15}\right)\left(8-\sqrt{15}\right)}}{2}\)

              \(2+\sqrt{64-15}=2+\sqrt{49}=2+7=9\) mà A>0

=> A=3

2) \(A=\sqrt{4-\sqrt{15}}\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right).\)

 \(A=\sqrt{\left(4-\sqrt{15}\right)\left(4+\sqrt{15}\right)}\sqrt{4+\sqrt{15}}\left(\sqrt{10}-\sqrt{6}\right).\)

​​\(A=\sqrt{4+\sqrt{15}}\left(\sqrt{10}-\sqrt{6}\right).\)

\(A^2=\left(4+\sqrt{15}\right)\left(16-4\sqrt{15}\right)\)

       \(=4\left(4+\sqrt{15}\right)\left(4-\sqrt{15}\right)=4\)

Mà A >0 

=> A=2

Mà 4>3

=> \(\sqrt{4}=2>\sqrt{3}\)

=> \(A>\sqrt{3}\)

a) 25¹⁵ và 8¹⁰. 3³⁰

25¹⁵ = (5² ) ¹⁵ = 5³⁰

8¹⁰. 3³⁰ = (2³ )¹⁰. 3³⁰ = 2³⁰. 3³⁰ = 6³⁰

Vì 5³⁰< 6³⁰

nên 25¹⁵< 8¹⁰. 3³⁰

b) \(\frac{4^{15}}{7^{30}}\)và \(\frac{8^{10}.3^{30}}{7^{30}.4^{15}}\)

\(\frac{4^{15}}{7^{30}}=\frac{\left(2^2\right)^{15}}{7^{30}}=\frac{2^{30}}{7^{30}}\)

\(\frac{8^{10}.3^{30}}{7^{30}.4^{15}}=\frac{\left(2^3\right)^{10}.3^{30}}{7^{30}.\left(2^2\right)^{15}}=\frac{2^{30}.3^{30}}{7^{30}.2^{30}}=\frac{3^{30}}{7^{30}}\)

Vì \(\frac{2^{30}}{7^{30}}< \frac{3^{30}}{7^{30}}\)

nên \(\frac{4^{15}}{7^{30}}< \frac{8^{10}.3^{30}}{7^{30}.4^{15}}\)

a)\(25^{15}=5^{2^{15}}=5^{30}\)

\(8^{10}.3^{30}=2^{3^{10}}.3^{30}=\left(2.3\right)^{30}=6^{30}\)

\(5^{30}< 6^{30}=>25^{15}< 8^{10}.3^{30}\)

b)\(\frac{4^{15}}{7^{30}}=\frac{2^{2^{15}}}{7^{30}}=\frac{2^{30}}{7^{30}}=\left(\frac{2}{7}\right)^{30}\)

\(\frac{8^{10}.3^{30}}{7^{30}.4^{15}}=\frac{2^{30}.3^{30}}{7^{30}.2^{30}}=\frac{6^{30}}{14^{30}}=\left(\frac{6}{14}\right)^{30}=\left(\frac{3}{7}\right)^{30}\)

Vì hai số có mũ bằng 30 nên ta so sánh :\(\frac{2}{7}< \frac{3}{7}\)

=>\(\frac{4^{15}}{7^{30}}< \frac{8^{10}.3^{30}}{7^{30}.4^{15}}\).

bài này của lớp 7 à???

a) Ta có: \(25^{15}=\left(5^2\right)^{15}=5^{30}\)

               \(8^{10}.3^{30}=\left(2^3\right)^{10}.3^{30}\)\(=2^{30}.3^{30}=6^{30}\)

Vì \(5^{30}< 6^{30}\)nên \(25^{15}< 8^{10}.3^{30}\)

b) Ta có: \(\frac{4^{15}}{7^{30}}=\frac{\left(2^2\right)^{15}}{7^{30}}=\frac{2^{30}}{7^{30}}\)

\(\frac{8^{10}.3^{30}}{7^{30}.4^{15}}=\frac{\left(2^3\right)^{10}.3^{30}}{7^{30}.\left(2^2\right)^{15}}=\frac{2^{30}.3^{30}}{7^{30}.2^{30}}=\frac{3^{30}}{7^{30}}\)

Vì \(2^{30}< 3^{30}\)nên \(\frac{2^{30}}{7^{30}}< \frac{3^{30}}{7^{30}}\)hay \(\frac{4^{15}}{7^{30}}< \frac{8^{10}.3^{30}}{7^{30}.4^{15}}\)

_Học tốt_

rõ ràng ta chỉ cần so sánh giữa \(15^{30}+16^{12}+17^{50}-16^8\) và \(17^{30}+16^8+15^{50}-16^{12}\)

Áp dụng tính chất nếu a>b thì a-b>0 ta được:

   \(15^{30}+16^{12}+17^{50}-16^8\)- \(\left(17^{30}+16^8+15^{50}-16^{12}\right)\)

= \(\left(17^{50}-17^{30}\right)+\left(16^{12}+16^{12}\right)+\left(15^{30}-15^{50}\right)-\left(16^8+16^8\right)\)

= \(\left(17^{50}-17^{30}\right)+\left(15^{30}-15^{50}\right)+2\left(16^{12}-16^8\right)\)

Vì 17^50 - 17^30 > l 15^30 - 15^50 l 

nên \(\left(17^{50}-17^{30}\right)+\left(15^{30}-15^{50}\right)>0\)

=>\(15^{30}+16^{12}+17^{50}-16^8\)> \(17^{30}+16^8+15^{50}-16^{12}\)

=> Phân số thứ nhất > 1 và p/s thứ hai < 1

Lúc này bạn tự so sánh nha

Lời giải:

$\frac{-3}{8}.\frac{2}{15}+\frac{-3}{8}.\frac{13}{15}+1\frac{3}{8}$

$=\frac{-3}{8}(\frac{2}{15}+\frac{13}{15})+1+\frac{3}{8}$

$=\frac{-3}{8}.\frac{15}{15}+1+\frac{3}{8}=\frac{-3}{8}+1+\frac{3}{8}=1$

\(\frac{-7}{15}.\frac{5}{8}-\frac{2}{8}.\frac{7}{15}+\frac{1}{8}.\frac{-23}{15}=\frac{-7}{24}-\frac{7}{60}-\frac{23}{120}=-\frac{3}{5}\)

=-7/24-7/60+-23/120

=(-7/24-7/60)+-23/120

=-49/120+-23/120

=-3/5

tớ bấm máy tính hẳn hoi

\(=\frac{1}{8.15}\left(\left(-7\right).5-2.7+1.\left(-23\right)\right)=\frac{1}{8.15}\left(-35-14-23\right)\)

\(=\frac{1}{8.15}.\left(-72\right)=-\frac{9}{15}=-\frac{3}{5}\)

Vì (x - 2)² \(\ge\) 0 => (x - 2)² - 15 \(\ge\) 0 - 15 = -15

(x - 2) - 15 \(\ge-15\)

a) Ta so sanh (x-2)²-15 va -15

Hay: (x-2)² -15+15   va -15+15

Hay:  (x-2)²  va 0

Ta thay: (x-2)² lon hon hoac bang 0 nen suy ra:

(x-2)²-15  se lon hon hoac bang 15

b) Ta so sanh: 8/3 - |x+1/2|  va 3

Hay: 8/3 - 8/3 - |x+1/2|   va  3-8/3

Hay: - | x+1/2|  va  1/3

Ta thay: |x+1/2| lon hon hoac bang 0  => -|x+1/2| se be hon hoac bang 0

=> - | x+1/2| < 1/3

=> 8/3 - |x+1/2|  < 3

Quy oi!! sao ban hoc gioi qua vay!! Minh kham phuc ban luon do!!