solve-x-4-18x-35-0-by-using-substitution-x-u-v-

Question Number 78683 by berket last updated on 19/Jan/20

s o l v e x^{4} - 18 x - 35 = 0 b y u s i n g s u b s t i t u t i o n x = u + v

Commented by john santu last updated on 20/Jan/20

x = u + v \Rightarrow x^{3} = u^{3} + v^{3} + 3 u v (u + v)

x^{4} - 18 x - 35 = 0

x (x^{3} - 18) - 35 = 0

x (u^{3} + v^{3} + 3 u v x - 18) - 35 = 0

3 u v x^{2} + (u^{3} + v^{3} - 18) x - 35 = 0

Commented by MJS last updated on 20/Jan/20

x^{4} ?

Commented by john santu last updated on 20/Jan/20

x = \frac{18 - (u^{3} + v^{3}) \pm \sqrt{{(u^{3} + v^{3} - 18)}^{2} + 420 u v}}{6 u v}

h i h i h i \dots i {d o n}^{'} t k n o w

Commented by MJS last updated on 20/Jan/20

this is no solution as you know \dots

x = u + v leads to {Cardano}^{'} s solution for

x^{3} + p x + q = 0

in this case, for x^{3} \dots one solution is x = 5, so

I think {it}^{'} s a typo

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