a, \(\left(x-15\right)\left(x+15\right)-\left(x+2\right)^2-\left(x-5\right)^2\)

\(=x^2-225-x^2-4x-4-x^2+10x-25\)

\(=-x^2+6x-254\)

b, \(\left(2x-1\right)\left(2x+1\right)+\left(x+9\right)^2-\left(x-3\right)^2\)

\(=4x^2-1+x^2+18x+81-x^2+6x-9=4x^2+24x+71\)

c, \(\left(7x-3\right)^2-\left(x-5\right)\left(x+5\right)-\left(2x+4\right)^2\)

\(=49x^2-42x+9-x^2+25-4x^2-16x-16=44x^2-58x+18\)

 Nếu bn ko nhìn rõ thì ib vs mk nhé, mk sẽ gửi bản full cho bn.

Đấy nhé

\(\left(a+b\right)^3=a^3+b^3+3ab\left(a+b\right)\)

\(\Leftrightarrow2^3=2+3.2.ab\)

\(\Leftrightarrow ab=1\)

\(a^2+b^2=\left(a+b\right)^2-2ab=2^2-2.1=2\)

\(a^4+b^4=\left(a^2+b^2\right)^2-2a^2b^2=2^2-2.1=2\)

Làm hộ mình câu e) C/m GB/BC=HD/(HA+HC) là đc

a) ĐKXĐ : \(x\ne\pm1\)

Khi đó \(\frac{3x-2}{x-1}-\frac{x+3}{x+1}=2\)

=>  \(\frac{\left(3x-2\right)\left(x+1\right)-\left(x+3\right)\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}=\frac{2\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}\)

=> (3x - 2)(x + 1) - (x + 3)(x - 1) = 2(x - 1)(x + 1) 

<=> 3x² + x - 2 - (x² + 2x - 3) = 2x² - 2 

<=> 2x² - x + 1 = 2x² - 2

<=> x = 3 (tm)

Vạy x = 3 là nghiệm phương trình 

b) 4x² - 1 = (x - 5)(1 - 2x) 

<=> (2x - 1)(2x +1) = -(x - 5)(2x - 1)

<=> (2x - 1)(2x + 1) + (x - 5)(2x - 1) = 0

<=> (2x - 1)(2x + 1 + x - 5) = 0

<=> (2x - 1)(3x - 4) = 0

<=> \(\orbr{\begin{cases}2x-1=0\\3x-4=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=\frac{4}{3}\end{cases}}\)

Vậy \(x\in\left\{\frac{1}{2};\frac{4}{3}\right\}\)là nghiệm phương trình 

c) \(\frac{x-3}{3}-\frac{2x-1}{2}>2\)

<=> \(\frac{2\left(x-3\right)-3\left(2x-1\right)}{6}>\frac{12}{6}\)

<=> 2(x - 3) - 3(2x - 1) > 12

<=> 2x - 6 - 6x + 3 > 12

<=> -4x > 15

=> x < -15/4

Vậy x < -15/4 là nghiệm bất phương trình 

\(a=4,b=16,c=17\)

\(\Delta=16^2-4.4.17=-16< 0\)

<=> phương trình vô nghiệm

Ta  có x > 0 

=> |-5x| = -(-5x) = 5x

Khi đó M = |-5x| - 5x + 3 = 5x - 5x + 3 = 3

=> M = 3

=> Chọn C 

a, 4x² - 49 = 0

⇔⇔ (2x)² - 7² = 0

⇔⇔ (2x - 7)(2x + 7) = 0

⇔{2x−7=02x+7=0⇔⎧⎪ ⎪⎨⎪ ⎪⎩x=72x=−72⇔{2x−7=02x+7=0⇔{x=72x=−72

b, x² + 36 = 12x

⇔⇔ x² + 36 - 12x = 0

⇔⇔ x² - 2.x.6 + 6² = 0

⇔⇔ (x - 6)² = 0

⇔⇔ x = 6

e, (x - 2)² - 16 = 0

⇔⇔ (x - 2)² - 4² = 0

⇔⇔ (x - 2 - 4)(x - 2 + 4) = 0

⇔⇔ (x - 6)(x + 2) = 0

⇔{x−6=0x+2=0⇔{x=6x=−2⇔{x−6=0x+2=0⇔{x=6x=−2

f, x² - 5x -14 = 0

⇔⇔ x² + 2x - 7x -14 = 0

⇔⇔ x(x + 2) - 7(x + 2) = 0

⇔⇔ (x + 2)(x - 7) = 0

⇔{x+2=0x−7=0⇔{x=−2x=7