To solve:
2x^4 - 5x^2 + 3 = 0

Asked by vanij1301 | 4th Feb, 2017, 07:13: PM

Expert Answer:

begin mathsize 16px style 2 straight x to the power of 4 minus 5 straight x squared plus 3 space equals space 0
Put space straight x squared equals straight t rightwards double arrow straight x to the power of 4 equals straight t squared
rightwards double arrow 2 straight t squared minus 5 straight t plus 3 equals 0
rightwards double arrow 2 straight t squared minus 2 straight t minus 3 straight t plus 3 equals 0
rightwards double arrow 2 straight t left parenthesis straight t minus 1 right parenthesis minus 3 left parenthesis straight t minus 1 right parenthesis equals 0
rightwards double arrow left parenthesis straight t minus 1 right parenthesis left parenthesis 2 straight t minus 3 right parenthesis equals 0
rightwards double arrow straight t equals 1 space or space straight t equals 3 over 2
Resubstituting space comma space we space get
space straight x squared equals 1 space or space straight x squared equals 3 over 2
rightwards double arrow straight x equals plus-or-minus 1 space or space straight x equals plus-or-minus fraction numerator square root of 3 over denominator square root of 2 end fraction
So comma space straight x equals plus-or-minus 1 space or space straight x equals plus-or-minus fraction numerator square root of 6 over denominator 2 end fraction... left parenthesis Rationalising space the space denominator right parenthesis end style

Answered by Rebecca Fernandes | 4th Feb, 2017, 07:31: PM

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