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\(\Leftrightarrow\frac{6x+5}{12x+9}-\frac{3x-7}{12x-9}=\frac{4x^2+10x-7}{16x^2-9}.\)
\(\Leftrightarrow\frac{\left(6x+5\right)\left(12x-9\right)-\left(3x-7\right)\left(12x+9\right)}{\left(3.4.x\right)^2-\left(3.3\right)^2}=\frac{4x^2+10x-7}{16x^2-9}\)
\(\Leftrightarrow\frac{72x^2+6x-45-\left(36x^2-57x-63\right)}{3^2\left(16x^2-9\right)}=\frac{4x^2+10x-7}{16x^2-9}\)
ĐK: \(16x^2-9\ne0\Leftrightarrow x^2\ne\left(\frac{3}{4}\right)^2\Rightarrow x\ne\pm\frac{3}{4}\)
\(\Leftrightarrow72x^2+6x-45-36x^2+57x+63=36x^2+90x-63\)
\(\Leftrightarrow27x=81\Leftrightarrow x=3\)
a, \(A=-x^2-2x+3=-\left(x^2+2x-3\right)=-\left(x^2+2x+1-4\right)\)
\(=-\left(x+1\right)^2+4\le4\)
Dấu ''='' xảy ra khi x = -1
Vậy GTLN là 4 khi x = -1
b, \(B=-4x^2+4x-3=-\left(4x^2-4x+3\right)=-\left(4x^2-4x+1+2\right)\)
\(=-\left(2x-1\right)^2-2\le-2\)
Dấu ''='' xảy ra khi x = 1/2
Vậy GTLN B là -2 khi x = 1/2
c, \(C=-x^2+6x-15=-\left(x^2-2x+15\right)=-\left(x^2-2x+1+14\right)\)
\(=-\left(x-1\right)^2-14\le-14\)
Vâỵ GTLN C là -14 khi x = 1
Bài 8 :
b, \(B=x^2-6x+11=x^2-6x+9+2=\left(x-3\right)^2+2\ge2\)
Dấu ''='' xảy ra khi x = 3
Vậy GTNN B là 2 khi x = 3
c, \(x^2-x+1=x^2-x+\dfrac{1}{4}+\dfrac{3}{4}=\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\)
Dấu ''='' xảy ra khi x = 1/2
Vậy ...
c, \(x^2-12x+2=x^2-12x+36-34=\left(x-6\right)^2-34\ge-34\)
Dấu ''='' xảy ra khi x = 6
Vậy ...
Ta có:
a) A = x2 + 6x + 10 = (x2 + 6x + 9) + 1 = (x + 3)2 + 1 \(\ge\)1 \(\forall\)x
Dấu "=" xảy ra <=> x + 3 = 0 <=> x = -3
Vậy MinA = 1 <=> x = -3
b) B = 4x2 - 12x + 13 = 4(x2 - 3x + 9/4) + 4 = 4(x - 3/2)2 + 4 \(\ge\)4 \(\forall\)x
Dấu "=" xảy ra <=> x - 3/2 = 0 <=> x = 3/2
Vậy MinB = 4 <=> x = 3/2
a) 4x(3x-7)-6(2x2-5x+1)=12
=>4x.3x-4x.7-6.2x2-6.(-5x)-6.1=12
=>12x2-28x-12x2+30x-6=12
=>2x-6 =12
=>2x =12+6
=>2x =18
=>x =18:2
=>x =6
b)(5x+3)(4x-1)+(10x-7)(-2x+3)=27
=>5x.4x-5x.1+3.4x+3.(-1)+10x.(-2x)+10x.3-7.-(2x)-7.3=27
=>20x2-5x+12x-3-20x2+30x+14x-21=27
=>39x-36 =27
=>39x =27+36
=>39x =63
=>x =63:39
=>x =21/13
c) (8x-5)(3x+2)-(12x+7)(2x-1)=17
=>8x.3x+8x.2-5.3x-5.2-12x.2x-12x.(-1)+7.2x+7.(-1)=17
=>24x2+16x-15x-10-24x2+12x+14x-7=17
=>27x-17 =17
=>27x =17+17
=>27x =34
=>x =34:27
=>x =34/27
d) (5x+9)(6x-1)-(2x-3)(15x+1)=-190
=>30x2-5x+63x-9 - 30x2-2x-45x-3=-190
=>11x-12 =-190
=>11x =-190+12
=>11x =-178
=>x = -178:11
=>x =-178/11
\(\dfrac{6x+5}{12x+9}+\dfrac{3x-7}{9-12x}=\dfrac{4x^2+10x-7}{16x^2-9}\)
\(\Leftrightarrow\dfrac{6x+5}{3\left(4x+3\right)}-\dfrac{3x-7}{3\left(4x-3\right)}=\dfrac{12x^2+30x-21}{3\left(4x-3\right)\left(4x+3\right)}\)
\(\Leftrightarrow\left(6x+5\right)\left(4x-3\right)-\left(3x-7\right)\left(4x+3\right)=12x^2+30x-21\)
\(\Leftrightarrow24x^2-18x+20x-15-\left(12x^2+9x-28x-21\right)=12x^2+30x-21\)
\(\Leftrightarrow24x^2+2x-15-12x^2+19x+21=12x^2+30x-21\)
=>31x+6=30x-21
=>x=-27