Find all positive solutions to:

x^6 + 7x = 4x^4 - x^2 + 8

2 answers

x^6 - 4x^4 + x^2 + 7x - 8 = 0

Wolfram said there is a positive solution at
appr. x = 1.80445

http://www.wolframalpha.com/input/?i=x%5E6+-+4x%5E4+%2B+x%5E2+%2B+7x+-+8+%3D+0

what a mess, this would be horrible without technology .
I won't have access to this on a test. How can I work it on a calculator.