`C=-2x^2+x+1`

`C=-2(x^2-x/2)+1`

`C=-2(x^2-2*x*1/4+1/16)+1+1/8`

`C=-2(x-1/4)^2+9/8<=9/8`

Dấu "=" `<=>x=1/4.`

Ta có: \(C=-2x^2+x+1\)

\(=-2\left(x^2-2\cdot x\cdot\dfrac{1}{4}+\dfrac{1}{16}-\dfrac{9}{16}\right)\)

\(=-2\left(x-\dfrac{1}{4}\right)^2+\dfrac{9}{8}\le\dfrac{9}{8}\forall x\)

Dấu '=' xảy ra khi \(x=\dfrac{1}{4}\)

`x^4+3x^2-2=0`

Đặt `x^2=t(t>=0)`

`pt<=>t^2+3t-2=0`

`<=>t^2+3t+9/4=17/4`

`<=>(t+3/2)^2=17/4`

`<=>t+3/2=sqrt{17}/2(do \ t>=0=>t+3/2>=3/2)`

`<=>t=(sqrt{17}-3)/2`

`<=>x^2=(sqrt{17}-3)/2`

`<=>x=+-sqrt{(sqrt{17}-3)/2}`

x² + x - 12 = 0

⇔ x² + 4x - 3x - 12 = 0

⇔ (x² + 4x) - (3x + 12) = 0

⇔ x(x + 4) - 3(x + 4) = 0

⇔ (x + 4)(x - 3) = 0

⇔ x + 4 = 0 hoặc x - 3 = 0

*) x + 4 = 0

⇔ x = -4

*) x - 3 = 0

⇔ x = 3

A = x₁² + x₂² + x₁².x₂ + x₁.x₂²

= (-4)² + 3² + (-4)².3 + (-4).3²

= 16 + 9 + 48 - 36

= 37

\(x^2+x-12=0\)

△=\(1^2+4\times12=49>0\)

⇒ptr có 2 ngh phân biệt \(x_1;x_2\)

Theo hệ thức viet: x\(_1\)+x\(_2\)=-1 và x\(_1\)x\(_2\)=-12

Có A= x\(_1\)\(^2\)+\(x_2\)\(^2\)+x\(_1\)\(^2\)x\(_2\)+x\(_1\)x\(_2\)\(^2\)

        = (x\(_1\)+x\(_2\))\(^2\) + x\(_1\)\(x_2\)(\(x_1+\)x\(_2\)) -2x\(_1\)x\(_2\)

        = \(\left(-1\right)^2+\left(-12\right).\left(-1\right)-2\left(-12\right)=1+12+24=37\)

Của bạn đây ạ <3

tìm gtnn hay sao bạn?

đề là j thế

\(=\left(a^2+mab\right)+\left(nab+mnb^2\right)\)

\(=a\left(a+mb\right)+nb\left(a+mb\right)\)

\(=\left(a+mb\right)\left(a+nb\right)\)

Ta có: \(a^2+ab\left(m+n\right)+mnb^2\)

\(=a^2+abm+abn+mnb^2\)

\(=a\left(a+bm\right)+nb\left(a+bm\right)\)

\(=\left(a+bm\right)\left(a+bn\right)\)

Đăng lại đi bạn bị lỗi rồi

P= (1 - x^2 )/ (x+1 )+(2x^2 +x)/x +x^2

P=\(\dfrac{1-x^2}{x+1}+\dfrac{x\left(2x+1\right)}{x\left(x+1\right)}\)

P=\(\dfrac{1-x^2}{x+1}+\dfrac{2x+1}{x+1}\)

P=\(\dfrac{-x^2+2x+2}{x+1}\)

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

3x²+3x-2x²-4x=1+x²

3x²+3x-2x²-4x-x²=1

x=-1

vậy............

b, ( 5/2 - x ) ^2

=25/4-4/5x+x^2

c,( xy/2 - x/3 ) ( xy/2 + x/3)

=(xy/2)^2-(x/3)^2

c: \(\left(\dfrac{xy}{2}-\dfrac{x}{3}\right)\left(\dfrac{xy}{2}+\dfrac{x}{3}\right)=\dfrac{x^2y^2}{4}-\dfrac{x^2}{9}\)

e: \(\left(2x+3y\right)^2=4x^2+12xy+9y^2\)

b) \(\left(\dfrac{5}{2}-x\right)^2=\dfrac{25}{4}-5x+x^2\)

c) \(\left(\dfrac{xy}{2}-\dfrac{x}{3}\right)\left(\dfrac{xy}{2}+\dfrac{x}{3}\right)=\dfrac{x^2y^2}{4}-\dfrac{x^2}{9}\)

d) \(\left(3x+\dfrac{2}{3}yz\right)^2=9x^2+4xyz+\dfrac{4}{9}y^2z^2\)

e) \(\left(2x+3y\right)^2=4x^2+12xy+9y^2\)

f) \(\left(2x-y+2\right)^2=\left(2x-y\right)^2+4\left(2x-y\right)+2^2=4x^2+y^2+4-4xy+8x-4y\)