3-x-4x-3-x-4-find-x-

Question Number 143208 by Gbenga last updated on 11/Jun/21

3^{x} + 4 x - 3 = x^{4}

f i n d x

Answered by MJS_new last updated on 11/Jun/21

you can only approximate

3^{x} = x^{4} - 4 x + 3

f (x) = 3^{x} is strictly increasing \forall x \in R

g (x) = x^{4} - 4 x + 3 has an absolute minimum

at (\begin{matrix} 1 \\ 0 \end{matrix}) and is strictly decreasing for x < 1

and strictly increasing for x > 1

f (0) = 1 \land g (0) = 3 \Rightarrow we have to search for x > 0

f (8) = 6561 \land g (8) = 4067 \Rightarrow x < 8

I get

x_{1} \approx . 376830

x_{2} \approx 1.87395

x_{3} \approx 7.15659

Commented by Gbenga last updated on 11/Jun/21

t h a n k s

Commented by Gbenga last updated on 11/Jun/21

f i n d x i n x + e^{x} + x^{4} - 4 = 0

Commented by mr W last updated on 11/Jun/21

t h e r e i s n o s t a n d a r d e x a c t w a y f o r

s o l u t i o n! t h e r e f o r e m o r e s u c h

q u e s t i o n s m a k e n o s e n s e .

y o u m a y a s k a s n e x t

f i n d x i n x + e^{- x} + x^{4} - 4 = 0

f i n d x i n x + \sin x + x^{4} - 4 = 0

f i n d x i n x + \cosh x + x^{4} - 4 = 0

\dots \dots

Commented by Gbenga last updated on 12/Jun/21

0 k s i r

Commented by Gbenga last updated on 12/Jun/21

b u t i t w a s a l s o s e n t t o m e b y a f r i e n d

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