If \(x^4+{1 \over x^4}=322\), then what is the value of \(x-{1 \over x}\)?
Answer
Correct Answer : b ) 4
Explanation :Consider the given equation
\(x^4+{1 \over x^4}=322\)
We know, that
(a + b)2 = a2 + b2 + 2ab
Thus,
\(x^4+{1 \over x^4} +2=322 +2\)
⇒\((x^2+{1 \over x^2})^2=324\)
⇒\((x^2+{1 \over x^2})=18 ............(2)\)
Now, using identity
(a – b)2 = a2 + b2 – 2ab
We get,
⇒\((x^2+{1 \over x^2}) -2=18-2\)
⇒\((x -{1 \over x^2})^2=16\)
⇒\((x-{1 \over x})=4\)
Hence, (b) is the correct answer.
Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, UPSC NDA etc.
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