Question : If $\left(w+\frac{1}{w}\right)=6$, then what will be the value of $\left(w-\frac{1}{w}\right)?$
Option 1: $4 \sqrt{2}$
Option 2: $\sqrt{2}$
Option 3: $3 \sqrt{2}$
Option 4: $2 \sqrt{2}$
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Correct Answer: $4 \sqrt{2}$
Solution : Given: $\left(w+\frac{1}{w}\right)=6$ Squaring both sides, we have, ⇒ $\left(w+\frac{1}{w}\right)^{2}=6^{2}$ ⇒ $w^{2}+\frac{1}{w^{2}}+2=36$ ⇒ $w^{2}+\frac{1}{w^{2}}=34$ ⇒ $w^{2}+\frac{1}{w^{2}}-2=34-2$ ⇒ $(w-\frac{1}{w})^{2}=32$ ⇒ $(w-\frac{1}{w})=\sqrt{32}$ $\therefore(w-\frac{1}{w})=4\sqrt{2}$ Hence, the correct answer is $4\sqrt{2}$.
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