Attempt this question from Algebra

Question of The Day15-03-2021

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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