Question

七年级数学题2道(100分)已知：A^X+A^Y=4 A^X+Y=2 求 1 A^2X+A^2Y 2 A^3X+A^3Y

Answer 1

A^X+A^Y=4

A^(X+Y)=2

1.

A^2X+A^2Y

=(A^X+A^Y)^2-2A^XA^Y

=4^2-2A^(X+Y)

=16-2*2

=16-4

=12

2.

A^3X+A^3Y

=(A^X+A^Y)(A^2X-A^X*A^Y+A^2Y)

=4[(A^2X+A^2Y)-A^(X+Y)]

=4(12-2)

=4*10

=40

X^4+2X+1

=X^4-2X^2+1+2X^2+2X

=(X^2-1)^2+2X(X+1)

=(X+1)^2(X-1)^2+2X(X+1)

=(X+1)[(X+1)(X-1)^2+2X]

=(X+1)[(X+1)(X^2-2X+1)+2X]

=(X+1)(X^3-2X^2+X+X^2-2X+1+2X)

=(X+1)(X^3-X^2+X+1)