Question

If between two numbers which are root of
given equation. x2 - 18x + 16 = 0, a GM is
inserted then the value of that GM is?
Select one:
a. 4
b. 5
C. 16
d. 6​

Answer 1

Answer:

C) 16

Step-by-step explanation:

Plz, refer to the picture for step by step answer!

PS: I have used a shortcut of GM. Actual formula for GM is

$\sqrt[n]{x1 \times x2 \times x3......... \times xn }$

Answer 2

Concept:

By calculating the root of the product of their values, the Geometric Mean (GM) denotes the central tendency of a collection of numbers. Essentially, we add all of the 'n' values together and subtract the nth root, where n is the total number of values.

Given:

The given equation is x²-18x+16 = 0.

Find:

The GM of the root of the given equation.

Solution:

x²-18x+16=0

a = 1, b = -18 and c= 16.

$x = \frac{-b + \sqrt{b^{2}-4ac } }{2a} \\\\x = \frac{18 + \sqrt{18^{2}-4*1*16 } }{2*1} \\\\x = \frac{18 + \sqrt{324-64 } }{2}\\\\ x = \frac{18 + \sqrt{260 } }{2} \\\\ x = \frac{18 +2 \sqrt{65 } }{2} \\\\\\x = 9+\sqrt{65}$

The other root will be

$x = \frac{-b-\sqrt{b^{2}-4ac } }{2a}\\ x = 9-\sqrt{65}$

The GM of the roots will be the square root of the products of the roots of the equation.

GM = √[(9+√65)(9-√65)]

      = √[81-65]

      = √16

      = 4

Hence, the GM of the roots is 4.