Nếu \(\frac{4x}{2^{x+y}}\)= 8 và \(\frac{9^{x+y}}{3^{5y}}\)= 243 thì x.y bằng bao nhiêu
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\(x^3-10x-12=\left(x^3-2x^2-6x\right)+\left(2x^2-4x-12\right)\)
\(=x\left(x^2-2x-6\right)+2\left(x^2-2x-6\right)=\left(x+2\right)\left(x^2-2x-6\right)\)
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\(a^4+a^2+1=\left(a^4+2a^2+1\right)-a^2=\left(a^2+1\right)^2-a^2=\left(a^2+1-a\right)\left(a^2+1+a\right).\)
Ta có x4 + x2 + 1 = (x4 + x3 + x2) + (- x3 - x2 - x) + ( x2 + x + 1) = x2( x2 + x + 1) - x( x2 + x + 1) + ( x2 + x + 1)
= ( x2 + x + 1)(x2 - x + 1)
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\(a\left(b^3-c^3\right)+b\left(c^3-a^3\right)+c\left(a^3-b^3\right)\)
\(=a\left[-\left(a^3-b^3\right)-\left(c^3-a^3\right)\right]+b\left(c^3-a^3\right)+c\left(a^3-b^3\right)\)
\(=-a\left(a^3-b^3\right)+c\left(a^3-b^3\right)+b\left(c^3-a^3\right)-a\left(c^3-a^3\right)\)
\(=\left(a^3-b^3\right)\left(c-a\right)+\left(c^3-a^3\right)\left(b-a\right)\)
\(=\left(a-b\right)\left(c-a\right)\left(a^2+ab+b^2\right)+\left(c-a\right)\left(b-a\right)\left(c^2+ac+a^2\right)\)
\(=\left(a-b\right)\left(c-a\right)\left(a^2+ab+b^2-c^2-a^2-ac\right)\)
\(=\left(a-b\right)\left(c-a\right)\left[\left(b-c\right)\left(b+c\right)+a\left(b-c\right)\right]\)
\(=\left(a-b\right)\left(c-a\right)\left(b-c\right)\left(a+b+c\right)\)
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Có: \(AB=BC.\sin C\)
\(\Rightarrow AB=10.\sin\left(30^{\text{o}}\right)\)
\(\Rightarrow AB=5\)
Đơn vị k rõ
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