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Question 74
If $$\left(X + \frac{1}{x} = 10\right)$$, what is the value of $$\left(x^{4} + \frac{1}{x^{4}}\right)$$?
Solution
$$x + \frac{1}{x} = 10$$
On squaring both sides.
We get
$$\left(x+\frac{1}{x}\right)^2=10^2$$
$$\left(x^2+\frac{1}{x^2}+2\right)=100$$
$$\left(x^2+\frac{1}{x^2}\right)=98$$
Again squaring both sides. We get:
$$\left(x^2+\frac{1}{x^2}\right)^2=98^2$$
$$(x^4+\frac{1}{x^4}+2)=9604$$
$$x^4+\frac{1}{x^4}=9602$$
This is a question from previous year actual exam. The question is incorrect in the exam itself.
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