Question

Find the value of $17{{x}^{7}}+{{x}^{7}}+x$ if $x=7$

Answer 1

Hint: Simplify the given expression further as the expression is not given in the simplest form in the question. Then substitute $x=7$ in the expression reduced to the simplest form to get the final answer.


Complete step-by-step answer:
In this question, we need to find the value of the expression $17{{x}^{7}}+{{x}^{7}}+x$ when we are given that $x=7$.

Let us first assign the given expression to \[f\left( x \right)\] .
So, we will have the following:
Let \[f\left( x \right)=17{{x}^{7}}+{{x}^{7}}+x\]

Now, we will simplify this function. After simplifying, we will have the following:
\[\Rightarrow f\left( x \right)=18{{x}^{7}}+x\]

Now we will substitute the value of x given in the question: $x=7$ in the given function: \[f\left( x \right)=18{{x}^{7}}+x\]
On substituting the value of x given in the question: $x=7$ in the given function: \[f\left( x \right)=18{{x}^{7}}+x\] , we will get the following:
\[f\left( 7 \right)=18{{\left( 7 \right)}^{7}}+7\] …(1)
Now, we will evaluate \[{{7}^{7}}=823543\]
We will now multiply this by 18 to change it to the form which is given in the function.
And so, \[18{{\left( 7 \right)}^{7}}=14823774\]

We will substitute this in equation (1). We will get the following:
\[f\left( 7 \right)=18{{\left( 7 \right)}^{7}}+7\]
\[f\left( 7 \right)=14823774+7\]
\[f\left( 7 \right)=14823781\]

Hence, the value of $17{{x}^{7}}+{{x}^{7}}+x$ when $x=7$ is \[14823781\].

Note:
The question is straight forward. You just need to first reduce the expression to the simplest form and then substitute $x=7$in the expression reduced to the simplest form to get the final answer. But the calculations involved are very lengthy. So check the calculations after each step and try to avoid any mistakes.