Question

if
$1 \\ {9x}^{2} \\ {3x}^{2}+ 14 \\ 4x + 21$
are in AP, then x is equal to​

Answer 1

EXPLANATION.

9x², 3x² + 14, 4x + 21  are in ap.

As we know that,

Conditions of an ap.

⇒ 2b = a + c.

Using this formula in this question, we get.

⇒ 2(3x² + 14) = 9x² + 4x + 21.

⇒ 6x² + 28 = 9x² + 4x + 21.

⇒ 9x² + 4x + 21 - 6x² - 28 = 0.

⇒ 9x² - 6x² + 4x + 21 - 28 = 0.

⇒ 3x² + 4x - 7 = 0.

Factorizes the equation into middle term splits, we get.

⇒ 3x² + 7x - 3x - 7 = 0.

⇒ x(3x + 7) - 1(3x + 7) = 0.

⇒ (x - 1)(3x + 7) = 0.

⇒ x = 1  and  x = - 7/3.

∴ The value of x = 1  and  x = - 7/3.