Tương tự 3. HS tự làm.

toán 8 nhé bạn
dùng Hằng đẳng thức đáng nhớ số 2

nâng cao bạn ạ

\(x^2-2\sqrt{13}x+13=0\)

\(x^2-2\cdot x\cdot\sqrt{13}+\left(\sqrt{13}\right)^2=0\)

\(\left(x-\sqrt{13}\right)^2=0\)

\(\Rightarrow x-\sqrt{13}=0\)

\(\Rightarrow x=\sqrt{13}\)

Vậy........

\(x=\sqrt{5+\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5+\sqrt{13+...}}}}}}\)

\(\Leftrightarrow x=\sqrt{5+\sqrt{13+x}}\) (\(x\ge0\))

\(\Leftrightarrow x^2=5+\sqrt{13+x}\)

\(\Leftrightarrow x^2-9=\sqrt{13+x}-4\)

\(\Leftrightarrow\left(x-3\right).\left(x+3\right)=\dfrac{x-3}{\sqrt{13+x}+4}\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x+3=\dfrac{1}{\sqrt{x+13}+4}\left(∗\right)\end{matrix}\right.\)

Xét (*) ta có VT \(\ge3\) (1)

mà \(VP=\dfrac{1}{\sqrt{x+13}+4}\le\dfrac{1}{4}\) (2)

Từ (1) và (2) dễ thấy (*) vô nghiệm 

Hay x = 3

f)

\(A=\sqrt{\frac{\left(x+1\right)}{x-3}}=\sqrt{1+\frac{4}{x-3}}\)

x-3={-4)=> x=-1

(82 - 5.x) : 13 - 4 = 0

(82 - 5.x) : 13 = 0 + 4

(82 - 5.x) : 13 = 4

(82 - 5.x) = 4 . 13

(82 - 5.x) = 52

5.x  = 82 - 52

5.x = 30

x = 30 : 5 = 6

(32 . 45) : 2 = (x + 70) : 14 - 40

720 = (x + 70) : 14 - 40

(x + 70) : 14 = 720 + 40

(x + 70) : 14 = 760

(x + 70) = 760 . 14

(x + 70) = 10640

x = 10640 - 70

x = 10570

Tìm x biết : 

( 82 - 5 . x ) : 13 - 4 = 0 

( 82 - 5 . x ) : 13 = 0 + 4 

( 82 - 5 . x )  : 13 = 4 

82 - 5 . x = 4 × 13 

82 - 5 . x = 52 

5 . x = 82 - 52 

5 . x = 30 

x = 30 : 5 

x = 6

Vậy x = 6

  a) ( 82- 5x ): 13- 4= 0

( 82- 5x ): 13           = 0+ 4

( 82- 5x ): 13           = 4

82- 5x                      = 4. 13

82- 5x                      = 52

5x                            =  82- 52

5x                            = 30

x                              = 30: 5

x                              = 6

  b) ( 32. 45 ): 2= ( x+ 70 ): 14- 40

1440: 2             = ( x+ 70 ): 14- 40

720                    = ( x+ 70): 14- 40

   => ( x+ 70 ): 14= 720+ 40

( x+ 70 ): 14       = 760

x+ 70                  = 760. 14

x+ 70                  = 10640

x                         = 10640- 70

x                         = 10570

\(\left(a\right):2x-7\sqrt{x}+3=0\left(x\ge0\right)\\ < =>\left(2x-6\sqrt{x}\right)-\left(\sqrt{x}-3\right)=0\\ < =>2\sqrt{x}\left(\sqrt{x}-3\right)-\left(\sqrt{x}-3\right)=0\\ < =>\left(2\sqrt{x}-1\right)\left(\sqrt{x}-3\right)=0\\ =>\left[{}\begin{matrix}2\sqrt{x}-1=0\\\sqrt{x}-3=0\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x=\dfrac{1}{4}\left(TM\right)\\x=9\left(TM\right)\end{matrix}\right.\)

\(\left(b\right):3\sqrt{x}+5< 6\\ < =>3\sqrt{x}< 1\\ < =>\sqrt{x}< \dfrac{1}{3}\\ < =>0\le x< \dfrac{1}{9}\)

\(\left(c\right):x-3\sqrt{x}-10< 0\\ < =>\left(x-5\sqrt{x}\right)+\left(2\sqrt{x}-10\right)< 0\\ < =>\sqrt{x}\left(\sqrt{x}-5\right)+2\left(\sqrt{x}-5\right)< 0\\ < =>\left(\sqrt{x}-5\right)\left(\sqrt{x}+2\right)< 0\\ =>\left\{{}\begin{matrix}\sqrt{x}-5< 0\\\sqrt{x}+2>0\end{matrix}\right.\\ < =>\left\{{}\begin{matrix}0\le x< 25\\x\ge0\end{matrix}\right.< =>0\le x< 25\)

\(\left(d\right):x-5\sqrt{x}+6=0\left(x\ge0\right)\\ < =>\left(x-2\sqrt{x}\right)-\left(3\sqrt{x}-6\right)=0\\ < =>\sqrt{x}\left(\sqrt{x}-2\right)-3\left(\sqrt{x}-2\right)=0\\ < =>\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)=0\\ =>\left[{}\begin{matrix}\sqrt{x}-3=0\\\sqrt{x}-2=0\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x=9\\x=4\end{matrix}\right.\left(TM\right)\)

\(\left(e\right):x+5\sqrt{x}-14< 0\\ < =>\left(x+7\sqrt{x}\right)-\left(2\sqrt{x}+14\right)< 0\\ < =>\sqrt{x}\left(\sqrt{x}+7\right)-2\left(\sqrt{x}+7\right)< 0\\ < =>\left(\sqrt{x}-2\right)\left(\sqrt{x}+7\right)< 0\\ =>\left\{{}\begin{matrix}\sqrt{x}+7>0\\\sqrt{x}-2< 0\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x\ge0\\0\le x< 4\end{matrix}\right.< =>0\le x< 4\)

Bài 1: Tìm x biết

a) x - 50 : 25 = 8     

x- 2 = 8 

x= 8+2

x=10

b) (x + 40).15 = 75.24

x+40 = 75.24:15

x+40 = 70

x= 30

c) (x - 32) - 15 = 0

x- 31 = 15

x= 15+ 31

x = 46

d) 1234 : x = 2

x= 1234:2

x = 617

e) (x - 34).26 = 0

x- 34 = 0: 26

x= 0 + 34

x= 34

f) 152 + (x + 231) : 2 = 358

(x+231):2 = 358- 152

(x+231):2 = 206

x+ 231 = 206*2

x= 412 - 231

x= 181 

1.

a) x - 50 : 25 = 8

x - 2 = 8

x = 10

b) (x + 40) . 15 = 75 . 24

x + 40 = 75 . 24 : 15

x + 40 = 120

x = 80

c) (x - 32) - 15 = 0

x - 32 = 15

x = 47

d) 1234 : x = 2

x = 617

e) (x - 34) . 26 = 0

Thỏa mãn điều kiện x - 34 = 0

x = 34

f) 152 + (x + 231) : 2 = 358

(x + 231) : 2 = 206

x + 231 = 412

x = 181

2.

a) 45 . (2 . x - 4) . 13 = 0

Thỏa mãn điều kiện 2 . x - 4 = 0

x = 2

b) 5 . x - 38 : 19 = 13

5 . x - 2 = 13

5 . x = 15

x = 3

c) 100 - 3 . (8 + x) = 1

3 . (8 + x) = 99

8 + x = 33

x = 25

d) [(x + 12) - 17] : 5 = 4

(x + 12) - 17 = 20

x + 12 = 37

x = 25

e) 84 - 4 . (2 . x + 1) = 48

4 . (2 . x + 1) = 36

2 . x + 1 = 9

2 . x = 8

x = 4

Bài 1: Tìm x biết

a) x - 50 : 25 = 8

<=> x - 2 = 8

<=> x = 10

Vậy x = 10

b) (x + 40).15 = 75.24

<=> x + 40 = 120

<=> x = 30

Vậy x = 30

c) (x - 32) - 15 = 0

<=> x - 32 = 15

<=> x = 47

Vậy x = 47

d) 1234 : x = 2

<=> x = 617

Vậy x = 617

e) (x - 34).26 = 0

<=> x - 34 = 0

<=> x = 34

Vậy x = 34

f) 152 + (x + 231) : 2 = 358

<=> (x + 231) : 2 = 206

<=> x + 231 = 412

<=> x = 181

Vậy x = 181

Bài 2: Trong tập hợp số tự nhiên, tìm x biết:

a) 45.(2.x - 4).13 = 0

<=> 2x - 4 = 0

<=> x = 2

Vậy x = 2

b) 5.x - 38 : 19 = 13

<=> 5x - 2 = 13

<=> x = 3

Vậy x = 3

c) 100 - 3.(8 + x) = 1

<=> 3(8 + x) = 99

<=>8 + x = 33

<=> x = 25

Vậy x = 25

d) [(x + 12)] - 17] : 5 = 4

<=> (x + 12) - 17 = 20

<=> x + 12 = 37

<=> x = 25

Vậy x = 25

e) 84 - 4.(2.x + 1) = 48

<=> 4(2x + 1) = 36

<=> 2x + 1 = 9

<=> x = 4

Vậy x = 4

Học tốt nhá :))