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How to solve 15(x^4)-30(L^2)(x^2)+7(L^4)=0?
3 Answers
- anordtugLv 67 years agoFavorite Answer
=15(x^4-2L^2 x^2+7/15 L^4)
=15((x^4-2L^2 x^2+L^4) - L^4+7/15 L^4)
=15((x^2-L^2)^2- 8/15 L^4)=0
(x^2-L^2)^2=8/15L^4
x^2-L^2=L^2*(8/15)^(1/2)
x^2=L^2*(1+(8/15)^1/2)
x=L(1+(8/15)^1/2)^1/2
- ?Lv 57 years ago
15(x^4)-30(L^2)(x^2)+7(L^4)=0
0) We first note that L is not zero, otherwise x^4 = 0, a trivial case.
1) Dividing both lhs and rhs by L^4 and letting y=x/L gives
15y^4 - 30 y^2 + 7 = 0
a quadratic equation in y^2.
2) Solving for y^2 by completing squares (looking for rational factors seems far too difficult)
3) Hence results for y...
