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设x+y+z =0,证明: x³ +y³ +z³ = 3xyz
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求4x+49y-28之平方根.
试解方程式 a(x+y)= b(x - y) = xy
Twos tations,A and B on opposite side of a mountain, are both visible from a third station C. The distance AC=3m.CB=5m and the angle ACB=60°. Find the distance between A and B.
Find all the positive angles less than 360° which satisfy the equation:cos2x+cosx+1=0
Homologous sides of two similar polygons have the ratio of 5 to 9 , the sum of the areas is 212 sq. ft. Find the area of each figure.
If two circles tangent at C and a common exterior tangent touches the circles in A and B, the angle ACB is a right angle.
Find the sum of the geometical series -2,,-1/3 to 6 terms.
Find the sum of the arithmetical series 49,44,39,… to 17 terms.
A motion picture film 120 feet long contains a certain number of individual pictures.If each picture were 0.1 of an inch shorter, the same film would contain 720 more pictures, how long is each picture?
Factor the following:4(a-b)²-12(a-b)(e+9e²)
英：If (1-x)n=c0+c1 x+c2 x2+⋯+cn xn, find the value of c0+2c1+3c2+⋯+(n+1) cn.汉：若(1-x)n=c0+c1 x+c2 x2+⋯+cn xn,求c0+2c1+3c2+⋯+(n+1) cn之值.
Factor the following expressions: a(b + c)² + b(c + a)² + c(a + b)² - 4abc
Factor the following expressions:x(y - z)³ + y(z -x)³ + z(x - y)³
Resolve (1+52x+30x2-24x3)/(3x2-x-1)2 into partial fractions.
If w is one of the imaginary cute roots of unity, show that the square of =hence show that the value of the determinant on the left is 3.
Factor the following:4a-16b+4a+1.
若 a² = ab,则a=b 对不对? 为什么?
设x为实数，试证：(x²-6x+5)/(x²+2x+1)之值不小于-1/3.
求下式之部分分式(2x+3)/((x-2)(x²+3)).
分解(x2-2x+5)/(x4-4x3+5x2-4x+4)为最简部分分式.
设 A,B 为 x 的两个有理整式，请用辗转相除法说明并证明何种情况为互质，何种情况下有公因式.有公因式时，说明求最高公因式之方法并证明之.
分解因式：a2-2ab+b2-6a+6b+5.
分解因式x2y - 2y3.
试分 ab(x²- y²)+ xy (a²-b²)为因数.
北京师范大学代数式
试将下列繁分数简单之：
有人定酒二坛，两坛所盛斤数不等，原定一盛甲酒每斤8角，一盛乙酒每斤5角.今误将甲坛盛乙酒，乙坛盛甲酒，酒商要求加洋一元五角.问两坛斤数各几何?
若a:b=c:d，试证(a2+b2):a3/(a+b)=(c2+d2):c3/(c+d).
化简((x2-y2)(2x2-2xy))/4(x-y)2-xy/(x+y)
约写下式A2/(A-B)(A-C)+B2/(B-C)(B-A)+C2/(C-A)(C-B).
