SOLUTION: find the number k>1 such that the region bounded by the curves y=1, y=x^-2, and x=k has area 6 square units.

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Question 1041796: find the number k>1 such that the region bounded by the curves y=1, y=x^-2, and x=k has area 6 square units.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
A+=+int%28%281-x%5E%28-2%29%29%2Cdx%2C1%2Ck%29+=+%28x%2B1%2Fx%291%5Ek+=+k+%2B+1%2Fk+-+2+=+6
===> k%5E2+%2B+1+-+2k+=+6k ===> k%5E2+-+8k+%2B+1+=+0
===> k+=+%288+%2B-+sqrt%28+64-4%2A1%2A1+%29%29%2F2+
==> k+=+%288+%2B+sqrt%28+64-4%2A1%2A1+%29%29%2F2++=+highlight%284%2Bsqrt%2815%29%29,
since 4+-+sqrt%2815%29+%3C+1.