Evaluate (a+b)2 , given a-b=8 and ab=10 .
Answer:
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Ta có: \(a+b=8\)
\(\Rightarrow\left(a+b\right)^2=8^2\)
\(\Rightarrow a^2+2ab+b^2=64\)
\(\Rightarrow a^2+2.10+b^2=64\)
\(\Rightarrow a^2+20+b^2=64\)
\(\Rightarrow a^2+b^2=44\)
\(\left(a-b\right)^2=a^2-2ab+b^2\)
\(=\left(a^2+b^2\right)-2.10\)
\(=44-20\)
\(=24\)
Vậy \(\left(a-b\right)^2=24\)
Evaluate the expression at
x3 + 12x + 48x + 64
= (x + 4)2
= (- 4 + 4)2
= 02
= 0
Fill in the blank: ............
x3 - a = (x - 2)(x2 + 2x + 4)
x3 - a = x3 - 8
a = 8
Fill in the blank: (x - 1)3 = x3 - 3x2 + 3x - 1 Fill in the blank: (x + 1)3 = x3 + 3x2 + 3x + 1Evaluate , given and .
Answer:
a + b = 8
(a + b)2 = 82
a2 + b2 + 2ab = 64
a2 + b2 + 2 . 10 = 64
a2 + b2 + 20 = 64
a2 + b2 = 64 - 20
a2 + b2 = 44
(a - b)2
= a2 - 2ab + b2
= 44 - 2 . 10
= 44 - 20
= 24
Given .
Evaluate A at .
Answer: A
A = (x - 5)(x2 + 5x + 25) - x2(x + 3) + 3x2
= x3 - 125 - x3 - 3x2 + 3x2
= - 125
Given .
Evaluate A at .
Answer: A
Answer: . Given and . Evaluate .Answer: a - b = 5(a - b)2 = 52a2 - 2ab + b2 = 25a2 + b2 - 2 . 4 = 25a2 + b2 - 8 = 25a2 + b2 = 25 + 8a2 + b2 = 33a3 - b3 = (a - b)(a2 + ab + b2) = 5 . (33 + 4)= 5 . 37= 185
Given and . Evaluate .
Answer: a + b = 5(a + b)2 = 52a2 + 2ab + b2 = 25a2 + b2 + 2 . 4 = 25a2 + b2 + 8 = 25a2 + b2 = 25 - 8a2 + b2 = 17a3 + b3= (a + b)(a2 - ab + b2)= 5 . (17 - 4)= 5 . 13= 65
\(\frac{x^3+x^2-4x-4}{x^3+8x^2+17x+10}=\frac{x^2\left(x+1\right)-4\left(x+1\right)}{x^2\left(x+1\right)+7x\left(x+1\right)+10\left(x+1\right)}\)
\(=\frac{\left(x+1\right)\left(x^2-4\right)}{\left(x+1\right)\left(x^2+7x+10\right)}=\frac{\left(x+2\right)\left(x-2\right)}{x\left(x+2\right)+5\left(x+2\right)}\)
\(=\frac{\left(x+2\right)\left(x-2\right)}{\left(x+2\right)\left(x+5\right)}=\frac{x-2}{x+5}\Rightarrow a=-2;b=5\)
\(\Rightarrow\)\(a+b=-2+5=3\)
giải
Ta có : \(\left(a+b\right)^2=\left(a-b\right)^2+4ab\)
Với \(a-b=8\)và \(ab=10\)
\(\Rightarrow\left(a+b\right)^2=8^2+4\times10\)
\(=104\)