bài nào zậy bạn

Câu 3 và caau4 bài giải phương trình nhé

Bài 3. Đặt ẩn phụ là 

\(a=2x-\frac{5}{x}\\\)

\(b=x-\frac{1}{x}\)

pt <=> \(b-a=\sqrt{a}-\sqrt{b}\\ \)

\(\left(\sqrt{b}-\sqrt{a}\right)\left(\sqrt{b}+\sqrt{a}\right)=-\left(\sqrt{b}-\sqrt{a}\right)\\ \)

\(\left(\sqrt{b}-\sqrt{a}\right)\left(\sqrt{b}+\sqrt{a}+1\right)=0\)

tới đây xét 2 TH bạn tự giải nhé

Do \(x^2+x+1=\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}>0;\forall x\) nên BPT tương đương:

\(-3\left(x^2+x+1\right)\le x^2-3x-1\le3\left(x^2+x+1\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2-3x-1\ge-3x^2-3x-3\\x^2-3x-1\le3x^2+3x+3\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}4x^2\ge-2\left(luôn-đúng\right)\\2x^2+6x+4\ge0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x\ge-1\\x\le-2\end{matrix}\right.\)

c: ĐKXĐ: x<>8

\(\dfrac{3}{2x-16}+\dfrac{3x-20}{x-8}+\dfrac{1}{8}=\dfrac{13x-102}{3x-24}\)

=>\(\dfrac{9}{6\left(x-8\right)}+\dfrac{18x-120}{6\left(x-8\right)}-\dfrac{26x-204}{6\left(x-8\right)}=\dfrac{-1}{8}\)

=>\(\dfrac{18x-111-26x+204}{6\left(x-8\right)}=\dfrac{-1}{8}\)

=>\(\dfrac{-8x+93}{6x-48}=\dfrac{-1}{8}\)

=>\(\dfrac{8x-93}{6x-48}=\dfrac{1}{8}\)

=>8(8x-93)=6x-48

=>64x-744-6x+48=0

=>58x=696

=>x=12

d: ĐKXĐ: x<>1; x<>-1

\(\dfrac{6}{x^2-1}+5=\dfrac{8x-1}{4x+4}+\dfrac{12x-1}{4x-4}\)

=>\(\dfrac{24}{4\left(x-1\right)\left(x+1\right)}+\dfrac{20\left(x^2-1\right)}{4\left(x-1\right)\left(x+1\right)}=\dfrac{\left(8x-1\right)\left(x-1\right)+\left(12x-1\right)\left(x+1\right)}{4\left(x-1\right)\left(x+1\right)}\)

=>8x^2-9x+1+12x^2+12x-x-1=24+20x^2-20

=>20x^2+2x=20x^2+4

=>2x=4

=>x=2(loại)

c: \(12\cdot3^x+3\cdot15^x-5^{x+1}=20\)

=>\(12\cdot3^x+3\cdot3^x\cdot5^x-5^x\cdot5-20=0\)

=>\(3^x\cdot3\left(5^x+4\right)-5\left(5^x+4\right)=0\)

=>\(\left(3^{x+1}-5\right)\left(5^x+4\right)=0\)

=>\(3^{x+1}-5=0\)

=>\(3^{x+1}=5\)

=>\(x+1=log_35\)

=>\(x=log_35-1\)

f: \(25^x-2\left(3-x\right)\cdot5^x+2x-7=0\)

=>\(\left(5^x\right)^2+5^x\cdot\left(2x-6\right)+2x-7=0\)

=>\(\left(5^x\right)^2+5^x\left(2x-7\right)+5^x+2x-7=0\)

=>\(5^x\left(5^x+2x-7\right)+\left(5^x+2x-7\right)=0\)

=>\(\left(5^x+1\right)\left(5^x+2x-7\right)=0\)

=>\(5^x+2x-7=0\)

Đặt \(A\left(x\right)=5^x+2x-7\)

=>\(A'\left(x\right)=5^x\cdot ln5+2>0\forall x\)

=>A(x) đồng biến trên R

=>A(x)=0 khi và chỉ khi x=1

i: \(9^x+2\left(x-2\right)\cdot3^x+2x-5=0\)

=>\(\left(3^x\right)^2+3^x\left(2x-5\right)+3^x+2x-5=0\)

=>\(\left(3^x+2x-5\right)\left(3^x+1\right)=0\)

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

Đặt \(B\left(x\right)=3^x+2x-5\)

=>\(B'\left(x\right)=3^x\cdot ln3+2>0\)

=>B(x) luôn đồng biến trên R

=>B(x)=0 khi và chỉ khi x=1

\(\left\{{}\begin{matrix}2x^2+y^2-2y+1=3-y^2\\2x^2+2x+2y^2-3y=4\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x^2+2y^2-2y=2\\2x^2+2y^2+2x-3y=4\end{matrix}\right.\)

Trừ vế cho vế:

\(2x-y=2\Rightarrow y=2x-2\)

Thế vào \(2x^2+2y^2-2y=2\Leftrightarrow x^2+y^2-y=1\) ta được:

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

\(\Leftrightarrow5x^2-10x+5=0\Rightarrow x=1\)

\(\Rightarrow y=0\)

Vậy nghiệm của hệ là: \(\left(x;y\right)=\left(1;0\right)\)

a, Th1 : \(m-1=0\Rightarrow m=1\)

\(\Rightarrow-x+3=0\\ \Rightarrow x=3\)

Th2 : \(m\ne1\)

\(\Delta=\left(-1\right)^2-4.\left(m-1\right).3\\ =1-12m+12\\=13-12m \)

phương trình có nghiệm \(\Delta\ge0\)

\(\Rightarrow13-12m\ge0\\ \Rightarrow m\le\dfrac{13}{12}\)

b, Áp dụng hệ thức vi ét : \(\left\{{}\begin{matrix}x_1+x_2=\dfrac{1}{m-1}\\x_1x_1=\dfrac{3}{m-1}\end{matrix}\right.\)

Tổng bình phương hai nghiệm bằng 12 \(\Rightarrow x^2_1+x^2_2=12\)

\(\left(x_1+x_2\right)^2-2x_1x_2=12\\ \Leftrightarrow\left(\dfrac{1}{m-1}\right)^2-2.\left(\dfrac{3}{m-1}\right)=12\\ \Leftrightarrow\dfrac{1}{\left(m-1\right)^2}-\dfrac{6}{m-1}=12\\ \Leftrightarrow1-6\left(m-1\right)=12\left(m-1\right)^2\\ \Leftrightarrow1-6m+6=12\left(m^2-2m+1\right)\\ \Leftrightarrow7-6m-12m^2+24m-12=0\\ \Leftrightarrow-12m^2+18m-5=0\\ \Leftrightarrow\left[{}\begin{matrix}m=\dfrac{9-\sqrt{21}}{12}\\m=\dfrac{9+\sqrt{21}}{12}\end{matrix}\right.\Rightarrow m=\dfrac{9+\sqrt{21}}{12}\)

\(\sqrt{4x-5}=\sqrt{3}\) (ĐKXĐ: \(x\ge\dfrac{5}{4}\))
\(\Rightarrow4x-5=3\)
\(\Rightarrow4x=8\)
\(\Rightarrow x=2\)(thỏa mãn)
Vậy x = 2
#gboy2mai

\(\sqrt{4x-5}=\sqrt{3}\left(ĐKXĐ:x\ge\dfrac{5}{4}\right)\)

\(\Rightarrow4x-5=3\)

\(\Leftrightarrow4x=8\)

\(\Leftrightarrow x=2\left(tm\right)\)

Vậy \(S=\left\{2\right\}\)

ĐKXĐ: x>=5/4

\(\sqrt{4x-5}=\sqrt{3}\)

=>4x-5=3

=>4x=8

=>x=8/4=2(nhận)

Có : G - T = 140 nu

   2T + 3G = 2520

=> A = T = 420 nu

G = X = 560 nu

N = 2 ( A + G ) = 1960 nu

l = N x 3,4 : 2 = 3332A^o

Ta có: \(G-T=140\)

          \(2T+3G=2520\)

\(\Rightarrow\left\{{}\begin{matrix}A=T=420nu\\G=X=560nu\end{matrix}\right.\)

\(N=2A+2G=2\cdot420+2\cdot560=1960nu\)

\(l=\dfrac{2N}{3,4}=\dfrac{2\cdot1960}{3,4}=1152,94A^o\)