- #1

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Then find the value of A^2 -B^2 + 1.

would i just take the the numbers and square them to get the value. What should i do.

- Thread starter woodworker101
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- #1

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Then find the value of A^2 -B^2 + 1.

would i just take the the numbers and square them to get the value. What should i do.

- #2

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for any [itex] A, B[/itex]

That should simplify it a great deal

- #3

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- #4

James R

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Then A = p+q and B = p-q

You want:

[tex]A^2 + B^2 - 1 = (p+q)^2 + (p-q)^2 - 1 = (p^2 + q^2 + 2pq) + (p^2 +q^2 - 2pq) - 1[/tex]

[tex]= 2p^2 + 2q^2 - 1 = 2(9^{9999}) + 2(9^{-9999}) - 1[/tex]

- #5

Curious3141

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Unnecessarily complicated, and I'm afraid you read the question wrongly.James R said:

Then A = p+q and B = p-q

You want:

[tex]A^2 + B^2 - 1 = (p+q)^2 + (p-q)^2 - 1 = (p^2 + q^2 + 2pq) + (p^2 +q^2 - 2pq) - 1[/tex]

[tex]= 2p^2 + 2q^2 - 1 = 2(9^{9999}) + 2(9^{-9999}) - 1[/tex]

[tex]A = 9^{9999} + 9^{-9999}[/tex] and [tex]B = 9^{9999} - 9^{-9999}[/tex]

[tex]A + B = (2)(9^{9999})[/tex] and [tex]A - B = (2)(9^{-9999})[/tex]

[tex]A^2 - B^2 + 1 = (A + B)(A - B) + 1 = (4)(9^{9999})(9^{-9999}) + 1 = 4 + 1 = 5[/tex]

- #6

James R

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I would argue that my solution is no more complicated than yours. You are, however, correct that I copied the question wrongly. My correct solution is:Curious3141 said:Unnecessarily complicated, and I'm afraid you read the question wrongly.

[tex]A^2 - B^2 + 1 = (p+q)^2 - (p-q)^2 + 1 = (p^2 + q^2 + 2pq) - (p^2 +q^2 - 2pq) + 1[/tex]

[tex]=4pq + 1 = 4(9^{9999})(9^{-9999}) + 1 = 4 + 1 = 5[/tex]

So, we agree.

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Thanks for the help.

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- #9

Curious3141

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I feel it's needlessly complicated to expand out the square terms, you can factorise immediately without doing that. With your notation, it would simply be :James R said:I would argue that my solution is no more complicated than yours. You are, however, correct that I copied the question wrongly. My correct solution is:

[tex]A^2 - B^2 + 1 = (p+q)^2 - (p-q)^2 + 1 = (p^2 + q^2 + 2pq) - (p^2 +q^2 - 2pq) + 1[/tex]

[tex]=4pq + 1 = 4(9^{9999})(9^{-9999}) + 1 = 4 + 1 = 5[/tex]

So, we agree.

[tex](p + q)^2 - (p - q)^2 + 1 = (p + q + p - q)(p + q - p + q) + 1 = (2p)(2q) + 1 = 4pq + 1[/tex]

and I personally think that is simpler, IMHO. But let's not split hairs.

- #10

James R

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Gee, I have a big ego! :)

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