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(P): y= -1/2x2
(d): y= x-3/2
(d'): y= mx+1/2
- xet’ PTHDGD ca (P) & (d)
-1/2x2 = x-3/2
=> -1/2x2 - x + 3/2 = 0
=> x = 1 ; x = 3
Thay x = 1 ; x = 3 vao (P)
=>y = -1/2 .12 = -1/2 ; y = -1/2 .(-3) 2 = -9/2
Vay giao diem cua (P) & (d) la (1 ; -1/2 ) (3 ; -9/2)
b.xet PTHDGD cua (P) & (d’)
mx+1/2 = -1/2x2
1/2x2 - mx -1/2 = 0
Δ = b2 - 4ac = (-m) 2 - 4.\(\frac{1}{2}\)\(\frac{1}{2}\) =m 2 - 1
De (P) txuc vs (d’) <=> Δ = 0 <=> m 2 - 1 = 0
<=>m = ± \(\sqrt{ }\)1
hinh nhu dung r day
\(\frac{1}{a+2}+\frac{3}{b+4}+\frac{2}{c+3}\le1\Leftrightarrow x+y+z\le1\)
\(Q=\left(\frac{1}{x}-1\right)\left(\frac{3}{y}-3\right)\left(\frac{2}{z}-2\right)=\frac{6\left(1-x\right)\left(1-y\right)\left(1-z\right)}{xyz}\ge\frac{6\left(y+z\right)\left(x+z\right)\left(x+y\right)}{xyz}\ge6.2.2.2=48\)
Min Q = 48 khi x =y=z = 1/3 => a =1 ; b =5; c =3
\(\frac{1}{a}+\frac{1}{c}=\frac{2}{b}\Leftrightarrow b=\frac{2ac}{a+c}\)
\(P=\frac{a+b}{2a-b}+\frac{b+c}{2c-b}=\frac{a+\frac{2ac}{a+c}}{2a-\frac{2ac}{a+c}}+\frac{\frac{2ac}{a+c}+c}{2c-\frac{2ac}{a+c}}=\frac{a+3c}{2a}+\frac{3a+c}{2c}=1+\frac{3}{2}\left(\frac{a}{c}+\frac{c}{a}\right)\ge4\)
Dấu "=" xảy ra khi \(a=b=c\)