Algebraic Manipulation

Algebraic Manipulation - Identities


If xx and yy are positive integers satisfying the equation 3x+5y=903x+5y=90, what is the maximum possible value of x+yx+y?

If the following equality always holds regardless of the value of kk, what is x+y+zx+y+z? (k2+k)x(k2k)y(k3)z=30?(k^2+k)x-(k^2-k)y-(k-3)z=30?

If positive integers xx and yy satisfy the equation xy5x10y+37=0xy-5x-10y+37=0, the sum x+yx+y is constant. What is the value of x+yx+y?

If a+b+c=1,a2+b2+c2=11,a+b+c=1, a^2+b^2+c^2=11, and abc=2,abc=2, what is the value of a2b2+b2c2+c2a2?a^2b^2+b^2c^2+c^2a^2?

If x8=829x^8 = 829, what is (x1)(x+1)(x2+1)(x4+1)(x-1)(x+1)(x^2+1)(x^4+1)?


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