tính giá trị của 135791^2+246824^2
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a: Khi x=2 và y=-3 thì \(x^2+2y=2^2+2\cdot\left(-3\right)=4-6=-2\)
b: \(A=x^2+2xy+y^2=\left(x+y\right)^2\)
Khi x=4 và y=6 thì \(A=\left(4+6\right)^2=10^2=100\)
c: \(P=x^2-4xy+4y^2=\left(x-2y\right)^2\)
Khi x=1 và y=1/2 thì \(P=\left(1-2\cdot\dfrac{1}{2}\right)^2=\left(1-1\right)^2=0\)
a) ĐKXĐ: x≠ \(\dfrac{1}{2}\); x≠ \(\dfrac{-1}{2}\); x≠0
A= \(\left(\dfrac{1}{2x-1}+\dfrac{3}{1-4x^2}-\dfrac{2}{2x+1}\right):\dfrac{x^2}{2x^2+x}\)
= \(\left(\dfrac{2x+1-3-2\left(2x-1\right)}{4x^2-1}\right):\dfrac{x^2}{2x^2+x}\)
= \(\left(\dfrac{2x+1-3-4x+2}{4x^2-1}\right):\dfrac{x^2}{2x^2+x}\)
= \(\dfrac{-4x}{\left(2x+1\right)\left(2x-1\right)}.\dfrac{x\left(2x+1\right)}{x^2}\)
= \(\dfrac{-4x^2}{x^2\left(2x-1\right)}\)
= \(\dfrac{-4}{2x-1}\)
b) Tại x= -2 ta có A= \(\dfrac{-4}{2.\left(-2\right)-1}\)= \(\dfrac{4}{5}\)
c) A= 4 ta có \(\dfrac{-4}{2x-1}\)=4
⇔ -4 = 4(2x-1)
⇔ -4 = 8x-4
⇔ x = 0
d) A=1 ta có \(\dfrac{-4}{2x-1}\)=1
⇔ -4 = 2x-1
⇔ x= \(\dfrac{-3}{2}\)
a: \(A=0x^2y^4z+\dfrac{7}{2}x^2y^4z-\dfrac{2}{5}x^2y^4z=\dfrac{31}{10}x^2y^4z=\dfrac{31}{10}\cdot2^2\cdot\dfrac{1}{16}\cdot\left(-1\right)=-\dfrac{31}{40}\)
a: \(=\dfrac{7}{5}x^4z^3y=\dfrac{7}{5}\cdot2^4\cdot\left(-1\right)^3\cdot\dfrac{1}{2}=-\dfrac{56}{5}\)
b: \(=-xy^3\)
\(Từ\) \(giả\) \(thiết\) : \(4a^2+b^2=\text{5}ab\)
\(\Leftrightarrow4a^2-4ab-ab+b^2\)
\(\Leftrightarrow\left(4a-b\right)\left(a-b\right)=0\)
\(TH1:\) \(4a-b=0\) \((\) \(mẫu\) \(thuẫn\) \(với\) \(2a>b\) \()\)
\(TH2:\) \(a-b=0\)
\(\Rightarrow a=b\)
\(\Rightarrow A=\dfrac{a^2}{4a^2-a^2}\)
\(\Rightarrow A=\dfrac{1}{3}\)
1) \(x^2-4x+5=x^2-4x+2^2+1=\left(x^2-4x+2^2\right)+1=\left(x-2\right)^2+1\)
Ta có : (x-2)2 >=0
=> (x-2)2+1>=1
Min A= 1 khi x=2
2) \(-x^2-2x+5=-\left(x^2+2x+1^2\right)+6=-\left(x+1\right)^2+6\)
(x+1)2>=0
=> -(x+1)2<=0
=> A<= 6
Max A = 6 khi x=-1
C1, x2 - 4x + 5
= ( x2 - 4x + 4 ) + 1
= ( x - 2 )2 + 1
=> (x -2)^2 + 1 lớn hơn hoặc bằng 1
=> x = 2
C2, -x2 - 2x + 5
= - (x2 - 2x - 1) - 4
= - (x - 1 ) 2 - 4
=> - (x - 1 ) 2 - 4 nhỏ hơn hoặc bằng 4
=> x = 1
C2 mình nghĩ vậy thôi chứ k chắc đâu
B1:
\(a,A=\left(\frac{3-x}{x+3}.\frac{x^2+6x+9}{x^2-9}+\frac{x}{x+3}\right):\frac{3x^2}{x+3}\)
\(=\left(\frac{\left(3-x\right)\left(x+3\right)^2}{\left(x+3\right)\left(x^2-9\right)}+\frac{x}{x+3}\right).\frac{x+3}{3x^2}\)
\(=\left(\frac{3-x}{x-3}+\frac{x}{x+3}\right).\frac{x+3}{3x^2}\)
\(=\left(\frac{\left(3-x\right)\left(x+3\right)}{x^2-9}+\frac{x\left(x-3\right)}{x^2-9}\right).\frac{x+3}{3x^2}\)
\(=\frac{3x+9-x^2-3x+x^2-3x}{x^2-9}.\frac{x+3}{3x^2}\)
\(=\frac{9-3x}{x^2-9}.\frac{x+3}{3x^2}\)
\(=\frac{3\left(3-x\right)\left(x+3\right)}{\left(x+3\right)\left(x-3\right)3x^2}\)
\(=\frac{3-x}{x^3-3x^2}\)
B2:
\(a,B=\left(\frac{x}{x^2-4}+\frac{2}{2-x}+\frac{1}{x+2}\right):\left(x-2+\frac{10-x^2}{x+2}\right)\)
\(=\left(\frac{x}{x^2-4}-\frac{2}{x-2}+\frac{1}{x+2}\right):\left(\frac{\left(x-2\right)\left(x+2\right)}{x+2}+\frac{10-x^2}{x+2}\right)\)
\(=\left(\frac{x}{x^2-4}-\frac{2\left(x+2\right)}{x^2-4}+\frac{x+2}{x^2-4}\right):\left(\frac{x^2-4+10-x^2}{x+2}\right)\)
\(=\left(\frac{x-2x-4+x-2}{x^2-4}\right):\frac{6}{x+2}\)
\(=-\frac{6}{x^2-4}.\frac{x+2}{6}\)
\(=\frac{-6\left(x+2\right)}{\left(x+2\right)\left(x-2\right)6}=-\frac{1}{x-2}\)
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