Find the roots of the equation 16x – \(\frac{10}{x}\) = 27

1.	Find the roots of the equation 16x – \(\frac{10}{x}\) = 27
Answer» Given, 16x – \(\frac{10}{x}\) = 27 On multiplying x on both the sides we have, ⇒ 16x² – 10 = 27x ⇒ 16x² – 27x – 10 = 0 ⇒ 16x² – 32x + 5x – 10 = 0 ⇒ 16x(x – 2) +5(x – 2) = 0 ⇒ (16x + 5) (x – 2) = 0 Now, either 16x + 5 = 0 ⇒ x = \(\frac{-5}{16}\) Or, x – 2 = 0 ⇒ x = 2 Thus, the roots of the given quadratic equation are x =\(\frac{-5}{16}\) and x = 2 respectively.

Answer»

Given,

16x – \(\frac{10}{x}\) = 27

On multiplying x on both the sides we have,

⇒ 16x² – 10 = 27x

⇒ 16x² – 27x – 10 = 0

⇒ 16x² – 32x + 5x – 10 = 0

⇒ 16x(x – 2) +5(x – 2) = 0

⇒ (16x + 5) (x – 2) = 0

Now, either 16x + 5 = 0 ⇒ x = \(\frac{-5}{16}\)

Or, x – 2 = 0 ⇒ x = 2

Thus, the roots of the given quadratic equation are x =\(\frac{-5}{16}\) and x = 2 respectively.

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