Discussion

Question:

If 5x - $\frac{1}{4 x}$ = 6, x > 0, then find the value of 25x² - $\frac{1}{16 x^{2}}$ ?

Explanation:

Given, 5x - $\frac{1}{4 x}$ = 6 ...(1)

Squaring both sides,

${(5 x - \frac{1}{4 x})}^{2}$ = 36

⇒ 25x² + $\frac{1}{16 x^{2}}$ - 2 × 5x × $\frac{1}{4 x}$ = 36

⇒ 25x² + $\frac{1}{16 x^{2}}$ + 2 × 5x × $\frac{1}{4 x}$ - 2 × 2 × 5x × $\frac{1}{4 x}$ = 36

⇒ ${(5 x + \frac{1}{4 x})}^{2}$ - 5 = 36

⇒ ${(5 x + \frac{1}{4 x})}^{2}$ = 41

⇒ 5x + $\frac{1}{4 x}$ = √41 ...(2)

From (1) × (2)

⇒ (5x)² - ${(\frac{1}{4 x})}^{2}$ = 6√41

Hence, option (a).

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