Ghi câu hỏi ra đi bn Nếu có thể mk sẽ giúp

a) \(x^2-15=\left(x-\sqrt{15}\right)\left(x+\sqrt{15}\right)\)

d) \(x-6\sqrt{x}+9-\left(\sqrt{x}-1\right)^2=\left(\sqrt{x}-3\right)^2-\left(\sqrt{x}-1\right)^2=\left(\sqrt{x}-3-\sqrt{x}+1\right)\left(\sqrt{x}-3+\sqrt{x}-1\right)=-2\left(2\sqrt{x}-4\right)=-4\left(\sqrt{x}-2\right)\)

1:

d: P=A+B

\(=\dfrac{2\sqrt{x}}{\sqrt{x}+3}+\dfrac{15-\sqrt{x}+2\sqrt{x}-10}{x-25}\cdot\dfrac{\sqrt{x}-5}{\sqrt{x}+3}\)

\(=\dfrac{2\sqrt{x}}{\sqrt{x}+3}+\dfrac{1}{\sqrt{x}+3}=\dfrac{2\sqrt{x}+1}{\sqrt{x}+3}\)

P nguyên

=>2căn x+6-5 chia hết cho căn x+3

=>căn x+3 thuộc Ư(-5)

=>căn x+3=5

=>x=4

3:

2: 

b: PTHĐGĐ là:

x^2-2(m+1)x+2m+1=0

Theo đề, ta có:

x1^2+x2^2=(căn 5)^2=5

=>(x1+x2)^2-2x1x2=5

=>(2m+2)^2-2(2m+1)=5

=>4m^2+8m+4-4m-2-5=0

=>4m^2+4m+1=0

=>m=-1/2

Lời giải:

c. Đặt $\sqrt{x}=a; \sqrt{y}=b$ thì:

$C=a^3-b^3+a^2b-ab^2=(a-b)(a^2+ab+b^2)+ab(a-b)$

$=(a-b)(a^2+ab+b^2+ab)=(a-b)(a^2+2ab+b^2)$

$=(a-b)(a+b)^2=(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y})^2$

Tính chất góc ngoài tam giác nhé. 

$x^2-2x-(x-7)(x+2)\\=x^2-2x-x^2+5x+14\\=3x+14$

Bài 1:

a. $(2x+5)(x-6)=2x^2-12x+5x-30$

$=2x^2-7x-30$

b. $(2x-1)(x^2-4x+3)=2x^3-8x^2+6x-x^2+4x-3$

$=2x^3-9x^2+10x-3$

c.

$x^2-2x-(x-7)(x+2)=x^2-2x-(x^2-5x-14)$

$=x^2-2x-x^2+5x+14=3x+14$

d.

$3x-(x+2)(x-4)=3x-(x^2-2x-8)$

$=3x-x^2+2x+8=-x^2+5x+8$

`a)A` có nghĩa `<=>x-1 >= 0 <=>x >= 1`

`b)B=\sqrt{3^2 .2}+\sqrt{2^3}-\sqrt{5^2 .2}`

`<=>B=3\sqrt{2}+2\sqrt{2}-5\sqrt{2}`

`<=>B=0`

`c)` Với `a >= 0,a \ne 1` có:

`C=[a-1]/[\sqrt{a}-1]-[a\sqrt{a}-1]/[a-1]`

`C=[(a-1)(\sqrt{a}+1)-a\sqrt{a}+1]/[(\sqrt{a}-1)(\sqrt{a}+1)]`

`C=[a\sqrt{a}+a-\sqrt{a}-1-a\sqrt{a}+1]/[(\sqrt{a}-1)(\sqrt{a}+1)]`

`C=a/[a-1]`