Sử dụng tính đơn điệu của hàm mũ: hàm \(y=a^x\) nghịch biến khi \(0< a< 1\) và đồng biến khi \(a>1\)

\(a^2=b^2+c^2\Rightarrow\left(\dfrac{b}{a}\right)^2+\left(\dfrac{c}{a}\right)^2=1\)

\(\Rightarrow\left\{{}\begin{matrix}0< \dfrac{b}{a}< 1\\0< \dfrac{c}{a}< 1\end{matrix}\right.\) nên các hàm \(\left(\dfrac{b}{a}\right)^x\) và \(\left(\dfrac{c}{a}\right)^x\) đều nghịch biến

Xét: \(\dfrac{b^m+c^m}{a^m}=\left(\dfrac{b}{a}\right)^m+\left(\dfrac{c}{a}\right)^m\) \(\)

- Khi \(m>2\Rightarrow\left(\dfrac{b}{a}\right)^m< \left(\dfrac{b}{a}\right)^2\) và \(\left(\dfrac{c}{a}\right)^m< \left(\dfrac{c}{a}\right)^2\)

\(\Rightarrow\left(\dfrac{b}{a}\right)^m+\left(\dfrac{c}{a}\right)^m< \left(\dfrac{b}{a}\right)^2+\left(\dfrac{c}{a}\right)^2=1\)

Hay \(\dfrac{b^m+c^m}{a^m}< 1\) \(\Rightarrow a^m>b^m+c^m\)

Câu b c/m tương tự, \(m< 2\) thì \(\left(\dfrac{b}{a}\right)^m>\left(\dfrac{b}{a}\right)^2...\)

`a vdots m,b vdots m`

`=>a+b vdots m`

Mà `a+b+c vdots m`

`=>a+b+c-(a+b) vdots m`

`=>a+b+c-a-b vdots m`

`=>(a-a)+(b-b)+c vdots m`

`=>0+0+c vdots m`

`=>c vdots m(forall a,b,c in Z)`

\(M=a\left(a+b\right)\left(a+c\right)=a\left(a^2+ac+ba+bc\right)\)

\(=a^3+a^2c+a^2b+abc=a^2\left(a+b+c\right)+abc\)

\(=a^20+abc=abc\) (1)

\(N=b\left(b+c\right)\left(b+a\right)=b\left(b^2+ba+cb+ca\right)\)

\(=b^3+b^2a+b^2c+abc=b^2\left(a+b+c\right)+abc\)

\(=b^20+abc=abc\) (2)

\(P=c\left(c+a\right)\left(c+b\right)=c\left(c^2+cb+ac+ab\right)\)

\(=c^3+c^2b+c^2a+abc=c^2\left(a+b+c\right)+abc\)

\(c^20+abc=abc\) (3)

từ (1);(2)và(3) ta có : \(M=N=P=abc\)

vậy khi \(\left(a+b+c\right)=0\)thì \(M=N=P\) (đpcm)

Chúc bạn học tốt !!!

ngay chỗ câu b em lộn xíu, EA = FA (2 cạnh tương ứng)

Ta có :a+b+c=0\(\Rightarrow\)\(\left\{{}\begin{matrix}a+b=-c\\a+c=-b\\b+c=-a\end{matrix}\right.\) (1)

Thay (1)vào M:\(\Rightarrow\) M = a(-c)(-b)=abc

Thay (1)vào N:\(\Rightarrow\) N = b(-a)(-c)=abc

Thay (1)vào P:\(\Rightarrow\) p = c(-b)(-a)=abc

\(\Rightarrow\)M=N=P

Ta có : \(a+b+c=0\)

\(\Rightarrow\left\{{}\begin{matrix}a+b=-c\\a+c=-b\\b+c=-a\end{matrix}\right.\)

\(M=a.\left(-c\right).\left(-b\right)=abc\)

\(N=b.\left(-a\right).\left(-c\right)=abc\)

\(P=c.\left(-b\right).\left(-a\right)=abc\)

\(\Rightarrow M=N=P\)

Find the word which has a different sound in the underlined part
1. A. class B. answer C. fat D. fast Âm a
2. A. great B. teacher C. stream D. meat Âm ea
3. A. dear B. wear C. nearly D. appear Âm ea
4. A. washes B. passes C. lakes D. couches Âm es
5. A. smile B. time C. kite D. miss Âm i
6. A. polluted B. prepared C. recycled D.watered Âm ed
7. A. the B. there C. think D. they Âm th
8. A. earth B. feather C. theater D. thanks Âm th
9. A. when B. where C. detective D. best Âm e
10. A. clumsy B. cute C. just D. but Âm u
11. A. weather B. newsreader C. teaching D. repeat Âm ea
12. A. game B. relax C. national D. channel Âm a
13. A. programme B. sport C. most D. show Âm o
14. A. thirty B. them C. both D. theme Âm th
15. A. schedule B. when C. red D. comedy Âm e

Find the word which has a different sound in the underlined part
1. A. class B. answer C. fat D. fast Âm a
2. A. great B. teacher C. stream D. meat Âm ea
3. A. dear B. wear C. nearly D. appear Âm ea
4. A. washes B. passes C. lakes D. couches Âm es
5. A. smile B. time C. kite D. miss Âm i
6. A. polluted B. prepared C. recycled D.watered Âm ed
7. A. the B. there C. think D. they Âm th
8. A. earth B. feather C. theater D. thanks Âm th
9. A. when B. where C. detective D. best Âm e
10. A. clumsy B. cute C. just D. but Âm u
11. A. weather B. newsreader C. teaching D. repeat Âm ea
12. A. game B. relax C. national D. channel Âm a
13. A. programme B. sport C. most D. show Âm o
14. A. thirty B. them C. both D. theme Âm th
15. A. schedule B. when C. red D. comedy Âm e