Asked by Anonymous
Solve the following inequality. Write the answer in interval notation.
x^4>4x^2
x^4>4x^2
Answers
Answered by
Reiny
x^4>4x^2
x^4 - 4x^2 > 0
x^2(x^2 - 4) > 0
x^2(x+2)(x-2) > 0
critical values are -2, 0, +2
for x < -2 , --->(+)(-)(-) >0 , so true
for x = 0 , no good
for -2 < x <0 , say x = -1
---> (+)(+)(-) < 0 , false
for 0 < x < 2 , ---> (+)(+)(-) < 0 , false
for x > 2, (+)(+)(+) > 0 , so true
solution:
x < -2 OR x > 2
check with Wolfram, see where the graph lies above the x axis.
http://www.wolframalpha.com/input/?i=plot+x%5E4+-+4x%5E2
x^4 - 4x^2 > 0
x^2(x^2 - 4) > 0
x^2(x+2)(x-2) > 0
critical values are -2, 0, +2
for x < -2 , --->(+)(-)(-) >0 , so true
for x = 0 , no good
for -2 < x <0 , say x = -1
---> (+)(+)(-) < 0 , false
for 0 < x < 2 , ---> (+)(+)(-) < 0 , false
for x > 2, (+)(+)(+) > 0 , so true
solution:
x < -2 OR x > 2
check with Wolfram, see where the graph lies above the x axis.
http://www.wolframalpha.com/input/?i=plot+x%5E4+-+4x%5E2
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