Question

3^{x}+4^{x} =5^{x}
then find the value of x

Answer 1

Answer:

x=35

Step-by-step explanation:

Answer 2

$\huge{\underline{\underline{\bf{Solution}}}}$

Value of x is 2.

$\rule{200}{2}$

$\tt given\begin{cases} \sf{3^x + 4^x = 5^x} \end{cases}$

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{To \: Find :}}}}$

We have to find the value of x.

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{Explanation :}}}}$

We will do this question by hit and trial method.

So, Put x = 0

$\sf{→3^0 + 4^0 = 5^0} \\ \\ \implies{\Large{\boxed{\rm{a^0 = 1}}}} \\ \\ \sf{→1 + 1 = 1} \\ \\ \sf{→2 ≠ 1}$

$\rule{150}{2}$

Now, Put x = 1

$\sf{→3^1 + 4^1 = 5^1} \\ \\ \sf{→3 + 4 = 5} \\ \\ \sf{→7 ≠ 5}$

$\rule{150}{2}$

Put x = 2

$\sf{→3^2 + 4^2 = 5^2} \\ \\ \sf{→9 + 16 = 25} \\ \\ \sf{→25 = 25}$

$\Large{\star{\boxed{\sf{x = 2}}}}$