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Question 32
If $$x^{4}+\frac{1}{x^{4}}= 198$$ and $$x>0$$, then what is the value of $$x^{2}-\frac{1}{x^{2}}$$?
Solution
Given : $$\ x^{4}+\frac{1}{x^{4}}\ =198$$
=> $$(x^2-\frac{1}{x^2})^2+2(x^2)(\frac{1}{x^2})=198$$
=> $$(x^2-\frac{1}{x^2})^2=198-2=196$$
=> $$x^2-\frac{1}{x^2}=\sqrt{196}=14$$
=> Ans - (A)
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