3-x-4-x-5-x-find-x-BY-ISHOLA-

Question Number 52091 by Olalekan99 last updated on 03/Jan/19

3^{x} + 4^{x} = 5^{x}

f i n d x

B Y I S H O L A

Commented by scientist last updated on 03/Jan/19

u s i n g b i n o m i a l e x p a n s i o n

{(1 + 2)}^{x} + {(1 + 3)}^{x} = {(1 + 4)}^{x}

Answered by scientist last updated on 03/Jan/19

x = 2

Answered by mr W last updated on 03/Jan/19

f (x) = 3^{x} + 4^{x} i s i n c r e a s i n g f u n c t i o n

g (x) = 5^{x} i s i n c r e a s i n g f u n c t i o n

f (1) = 3 + 4 = 7

g (1) = 5

f (1) > g (1)

f (3) = 3^{3} + 4^{3} = 91

g (3) = 5^{3} = 125

f (3) < g (3)

\Rightarrow t h e r e i s o n e a n d o n l y o n e s o l u t i o n b e t w e e n

1 a n d 3 f o r f (x) = g (x) .

s i n c e f (2) = 3^{2} + 4^{2} = 25 = 5^{2} = g (x),

t h e o n l y s o l u t i o n i s x = 2 .

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