5. If x + x-1 = a, express x2 + 2 + x-2 in terms of a.

Mathematics

1 answer:

yawa3891 [41]3 years ago

3 0

I suppose the question is, if $x+x^{-1}=a$ , what is $x^2+2+x^{-2}$ ?

Recall that $(a+b)^2=a^2+2ab+b^2$ . It follows that for $x\neq0$ ,

$x^2+2+x^{-2}=x^2+2xx^{-1}+(x^{-1})^2=(x+x^{-1})^2=\boxed{a^2}$

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Answer to problem 1 is (-4, 4)

Answer to problem 3 is (2, 2)

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Explanation:

When the center of a dilation is the origin (0,0), we simply multiply the scale factor by each coordinate.

For problem 1, point U is located at (-2,2). Multiply each coordinate by the scale factor 2 (since it says "dilation of 2") to get (-4,4)

For problem 3, we multiply 0.5 by each coordinate of the point U(4, 4) getting to U ' (2,2)

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The dilation rule used here is $(x,y) \to (kx, ky)$ where k is the scale factor or dilation factor. This rule only applies if the center of dilation is (0,0). For other centers, you'll need to apply a translation first, dilate, then translate back again.