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Bài 2:
\(a^2+b^2=\left(a+b\right)^2-2ab=5^2-2\cdot\left(-2\right)=9\)
\(\dfrac{1}{a^3}+\dfrac{1}{b^3}=\dfrac{a^3+b^3}{a^3b^3}=\dfrac{\left(a+b\right)^3-3ab\left(a+b\right)}{\left(ab\right)^3}\)
\(=\dfrac{5^3-3\cdot5\cdot\left(-2\right)}{\left(-2\right)^3}=\dfrac{125+30}{8}=\dfrac{155}{8}\)
\(a-b=-\sqrt{\left(a+b\right)^2-4ab}=-\sqrt{5^2-4\cdot\left(-2\right)}=-\sqrt{33}\)
Ta có \(a-b=5\Rightarrow\left(a-b\right)^2=25\Rightarrow a^2+b^2=25+2ab=25+2\cdot2=29\) (Do ab=2)
\(B=3\left[\left(a^2+b^2\right)^2-2a^2b^2\right]+2\left[\left(a-b\right)\left(a^4+b^4+a^3b^2+a^2b^3\right)\right]\)
= \(3\left[29^2-2\cdot4\right]+2\left\{5\left[\left(a^2+b^2\right)^2-2a^2b^2+ab\left(a^2+b^2\right)\right]\right\}\)
= 3\(\cdot833+10\left[29^2-2\cdot4+2\cdot29\right]\) \(=2499+10\cdot891=11409\)
\(A=a^2+b^2=\left(a+b\right)^2-2ab=3^2-2.\left(-5\right)=19\)
\(B=a^4+b^4=\left(a^2+b^2\right)^2-2\left(ab\right)^2=19^2-2.\left(-5\right)^2=311\)
- a) Ta có: a + b = 5 => a2 + b2 = 25 - 2ab
- Mặt khác: a3 + b3 = 35 => (a + b)( a^2 + b^2 - ab) = 5( 25 - 2ab - ab) = 125 - 15ab = 35
- => ab = 6
Bạn chỉ cần thay vào và làm câu b tương tự là đc nhé ^^
Ta có
x + y = 2
=> (x+y)^2 = 4
=> x^2 + 2xy + y^2 = 4
=> 10 + 2xy= 4
=> 2xy = -6
=> xy= -3
x^3 + y^3 = ( x+Y) ( x^2 - xy + y^2) = 2 ( 10 -- 3) = 2( 10 + 3 ) = 2.13 = 26
Ta có : \(a^3+b^3+3\left(a^2+b^2\right)+4\left(a+b\right)+4=0\)
\(=>\left(a+1\right)^3+\left(b+1\right)^3+a+b+2=0\)
\(=>\left(a+b+2\right)\left[\left(a+1\right)^2-\left(a+1\right)\left(b+1\right)+\left(b+1\right)^2\right]+\left(a+b+2\right)=0\)
\(=>\left(a+b+2\right)\left(a^2+b^2+a+b-ab+2\right)=0\)
\(=>\left(a+b+2\right)2\left(a^2+b^2+a+b-ab+2\right)=0\)
\(=>\left(a+b+2\right)\left(2a^2+2b^2+2a+2b-2ab+4\right)=0\)
\(=>\left(a+b+2\right)\left[\left(a-b\right)^2+\left(a+1\right)^2+\left(b+1\right)^2+2\right]=0\)
Lại có : \(\left(a-b\right)^2\ge0;\left(a+1\right)^2\ge0;\left(b+1\right)^2\ge0\)
\(=>\left(a-b\right)^2+\left(a+1\right)^2+\left(b+1\right)^2+2\ge0\)
\(=>a+b+2=0=>a+b=-2=>M=2018.\left(-2\right)^2=8072\)
ta có: a + b=-2 ; a^2 + b^2 = 52
=> (a+b)^2 = 4 => a^2 + 2ab + b^2 = 4
=> 52 + 2ab= 4
=> 48= -2ab
=> ab= -24
a^3 + b^3 = (a+b)( a^2-ab+ b^2)
=> a^3 + b^3 = -2.(52+24)= -2. 76= -152