If a - 12/a = 1, where a > 0, then the value of a² + 16/(a²) is :

If a - 12/a = 1, where a > 0, then the value of a² +…

If a - $\frac{12}{a}$ = 1, where a > 0, then the value of a² + $\frac{16}{a^2}$ is :

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Correct answer: B

Explanation

The correct answer is Option 2 i.e. 17.

Given, a - 12/a = 1

⇒ a² - 12 = a

⇒ a² - a - 12 = 0

⇒ a² - 4a + 3a - 12 = 0

⇒ a(a - 4) + 3(a - 4) = 0

⇒ a = 4, -3

but as given a > 0,

⇒ a = 4

Putting in a² + $\frac{16}{a^2}$ ,

⇒ 16 + 1 = 17