\(\sqrt{x}=1-\sqrt{3}\)

Nhận xét:

\(\sqrt{3}>\sqrt{1}=1\)

\(\Rightarrow1-\sqrt{3}< 0\)

\(\Rightarrow\sqrt{x}< 0\) (vô lí)

Vậy không tìm được giá trị x thoả mãn đề bài

\(\left(a+1\right)\left(a+2\right)\left(a+3\right)\left(a+4\right)+1\\ =\left[\left(a+1\right)\left(a+4\right)\right]\left[\left(a+2\right)\left(a+3\right)\right]+1\\ =\left(a^2+5a+4\right)\left(a^2+5a+6\right)+1\\ =\left(a^2+5a+4\right)\left(a^2+5a+4\right)+2\left(a^2+5a+4\right)+1\\ \left(a^2+5a+4\right)^2+2\left(a^2+5a+4\right)+1\\ =\left(a^2+5a+5\right)^2\)

It was a long time before we came _____to_____ the truth. 

(come to: đạt được, phát hiện ra điều gì đó)

The dog came _____at_____ us with teeth bared.

(come at: tiếp cận với thái độ hung hăng hoặc thù địch)

Come _____on_____ ! We are late for the bus.

(come on: đây là lời thúc giục di chuyển: nhanh lên)

How is your English coming ____along______ ?

(come along: phát triển, tiến đến)

I was picking up the teapot when it came __apart________ in my hands.

(come apart: rơi ra, tách ra, rời rạc)

She has been very ill, but now she is coming ___round_______ fine.

(com round: hồi phục, khôi phục)

We must not let this silly quarrel come ___between_______ us.

(come between: gây cản trở, tạo ra rào cản)

I come _____from_____ Liverpool, but I have spent most of my life in Scotland.

(come from: đến từ)

John has come __into________ the money; he inherited £5,000.

(come into: thừa kế)

The town came _____into_____ sight when we turned the bend.

(come into: xuất hiện)

The hook came ____off______ the wall when I hung up my coat

(come off: bong ra, rời ra)

This tool will come ____in______ very handy for my uncle.

(come in handy: có ích)

Snails come ____out______ as soon as it rains.

(come out: xuất hiện)

When did you first come ____over______ to Europe?

(come over: di chuyển)

Your talk came ______to____ very well.

(come to: kết quả là, dẫn đến)

It has come _____to_____ my attention that he is very short-tempered.

He came ______to____ the conclusion that someone was having an affair with his wife.

He came _______up___ and asked me if I had the time.

(come up: xảy ra, xuất hiện)

Much of the tea consumed in England comes __from________ Sri Lanka.

(come from: đến từ)

He comes ____from______ an interesting family.

How’s your orchard coming _____along_____ ?

Sometimes it’s very difficult to come ___to_______ the truth.

He never lets anything come ______between____ him and his morning paper.

It was a long time before we came ___to_______ the truth.
The dog came _____at_____ us with teeth bared.
Come ____on______ ! We are late for the bus.
How is your English coming ____along______ ?
I was picking up the teapot when it came ______âpart____ in my hands.
She has been very ill, but now she is coming ______round____ fine.
We must not let this silly quarrel come ____between______ us.
I come ______from____ Liverpool, but I have spent most of my life in Scotland.
John has come _____into_____ the money; he inherited £5,000.
The town came ______into____ sight when we turned the bend.

a) $-(2x-4)(x+2)+(x+2)^2+(x-2)^2-4x^2-1-4x=-3$

$\Leftrightarrow (x-2)^2-2(x-2)(x+2)+(x+2)^2-4x^2-4x+2=0$

$\Leftrightarrow (x-2+x+2)^2-4x^2-4x+2=0$

$\Leftrightarrow (2x)^2-4x^2-4x=-2$

$\Leftrightarrow -4x=-2$

$\Leftrightarrow x=\frac12$

b) $(4x-1)^2-16(x+1)(x+3)=25$

$\Leftrightarrow (4x)^2-2.4x.1+1^2-16(x^2+4x+3)=25$

$\Leftrightarrow 16x^2-8x+1-16x^2-64x-48=25$

$\Leftrightarrow -72x-47=25$

$\Leftrightarrow -72x=72$

$\Leftrightarrow x=-1$

c) $(3x-7)^2=9(3x-7)(x+5)+694$

$\Leftrightarrow (3x)^2-2.3x.7+7^2=9(3x^2+8x-35)+694$

$\Leftrightarrow 9x^2-42x+49=27x^2+72x-315+694$

$\Leftrightarrow 18x^2+114x+330=0$

$\Leftrightarrow 9x^2+57x+165=0$

$\Leftrightarrow 9\left(x+\frac{19}{6}\right)^2+\frac{299}{4}=0$ (vô lí)

=> Pt vô nghiệm

d) $(2x-1)^2+(x+3)^2=5(x+7)(x-7)-3x$

$\Leftrightarrow 4x^2-4x+1+x^2+6x+9=5(x^2-49)-3x$

$\Leftrightarrow 5x^2+2x+10=5x^2-3x-245$

$\Leftrightarrow 5x=-255$

$\Leftrightarrow x=-51$

#$\mathtt{Toru}$

a: \(-\left(2x-4\right)\left(x+2\right)+\left(x+2\right)^2+\left(x-2\right)^2-4x^2-1-4x=-3\)

=>\(-2\left(x^2-4\right)+x^2+4x+4+x^2-4x+4-4x^2-1-4x=-3\)

=>\(-2x^2+8-2x^2-4x+7+3=0\)

=>\(-4x^2-4x+18=0\)

=>\(x=\dfrac{-1\pm\sqrt{19}}{2}\)

b: \(\left(4x-1\right)^2-16\left(x+1\right)\left(x+3\right)=25\)

=>\(16x^2-8x+1-16\left(x^2+4x+3\right)-25=0\)

=>\(16x^2-8x-24-16x^2-64x-48=0\)

=>-72x-72=0

=>x=-1

c: \(\left(3x-7\right)^2=9\left(3x-7\right)\left(x+5\right)+694\)

=>\(9\left(3x^2+15x-7x-35\right)+694=9x^2-42x+49\)

=>\(27x^2+72x-315+694-9x^2+42x-49=0\)

=>\(18x^2+114x+330=0\)

=>\(x\in\varnothing\)

d: \(\left(2x-1\right)^2+\left(x+3\right)^2=5\left(x+7\right)\left(x-7\right)-3x\)

=>\(4x^2-4x+1+x^2+6x+9=5\left(x^2-49\right)-3x\)

=>\(5x^2+2x+10-5x^2+245+3x=0\)

=>5x+255=0

=>x+51=0

=>x=-51

Bài 7

1) 

\(A=8\left(3^2+1\right)\left(3^4+1\right)...\left(3^{16}+1\right)\\ =\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)....\left(3^{16}+1\right)\\ =\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\\ =\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)\\ =\left(3^{16}-1\right)\left(3^{16}+1\right)\\ =3^{32}-1\)

2)  

\(B=\left(1-3\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)...\left(3^{16}+1\right)\\ =-\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)...\left(3^{16}+1\right)\\ =-\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)...\left(3^{16}+1\right)\\ =-\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\\ =-\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)\\ =-\left(3^{16}-1\right)\left(3^{16}+1\right)\\ =-\left(3^{32}-1\right)\\ =1-3^{32}\)  

When I have free time, I usually read books. Except school time, books live with me for almost the rest of the day. There are some reasons why I love reading. The first reason is that it helps widen knowledge. I can access a wide range of knowledge such as literature, science, biology, … Next, I can reduce stress by reading funny stories. I have collected many comic books since I was 6. Moreover, it can give me an unlimited imagination, so I can write books in the future. I can learn the different cultures and customs of other countries in the world too. I read books at least one hour every day. I wish I could read all kinds of books over the world.

a: Ta có: \(AK=KB=\dfrac{AB}{2}\)

\(DI=IC=\dfrac{DC}{2}\)

mà AB=CD

nên AK=KB=DI=IC

Xét tứ giác AKCI có

AK//CI

AK=CI

Do đó: AKCI là hình bình hành

=>AI//CK và AI=CK

b: Xét ΔDNC có

I là trung điểm của DC

IM//NC

Do đó: M là trung điểm của DN

=>DM=MN

Xét ΔBAM có

K là trung điểm của BA

KN//AM

Do đó: N là trung điểm của BM

=>BN=NM

=>BN=NM=DM

c: Xét tứ giác BKDI có

BK//DI

BK=DI

Do đó: BKDI là hình bình hành

=>DK//BI

=>EK//FI

ta có: AI//CK

=>IE//KF

Xét tứ giác EKFI có

EK//FI

EI//KF

Do đó: EKFI là hình bình hành