SOLUTION: (3rd root 2)^(2-x)=2^x^2

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Question 1076933: (3rd root 2)^(2-x)=2^x^2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

+%28root%283%2C+2%29%29%5E%282-x%29=2%5E%28x%5E2%29

+%28+%282%5E%281%2F3%29%29%29%5E%282-x%29=2%5E%28x%5E2%29

+2%5E%28%281%2F3%29%282-x%29%29=2%5E%28x%5E2%29.........if base same, we have

+%281%2F3%29%282-x%29=x%5E2

+2-x=3x%5E2

+3x%5E2%2Bx-2=0

+3x%5E2%2B3x-2x-2=0

+%283x%5E2%2B3x%29-%282x%2B2%29=0

+3x%28x%2B1%29-2%28x%2B1%29=0

+%28x+%2B+1%29+%283x+-+2%29+=+0

solutions:

if +%28x+%2B+1%29+=+0=>x=-1->Integer solution
if ++%283x+-+2%29+=+0=>x=2%2F3->Real solution