Question

Please solve this question​

Answer 1

Step-by-step explanation:

in the salution in maths

Answer 2

$\large\underline{\sf{Solution-}}$

Before we solve this problem,

Let derive the relation-ship between Arithmetic mean and Geometric mean with two numbers a and b as a quadratic equation.

↝ Let assume that a and b are two positive numbers.

Then

↝ Arithmetic Mean, A between a and b is given by

$\rm :\longmapsto\:\boxed{ \tt{ \: A = \frac{a + b}{2} \: }}$

and

↝ The geometric mean, G between a and b is given by

$\rm :\longmapsto\:\boxed{ \tt{ \: G = \sqrt{ab} \: }}$

Now,

Quadratic equation having roots as a and b is given by

$\rm :\longmapsto\: {x}^{2} - (a + b)x + ab = 0$

can be rewritten as, on substitute the values of a + b and ab,

$\rm :\longmapsto\: {x}^{2} - 2Ax + {G}^{2} = 0$

So, Let's solve the problem !!!

Given quadratic equation is

$\rm :\longmapsto\: {x}^{2} - 10x + 11 = 0$

So, on comparing with

$\rm :\longmapsto\: {x}^{2} - 2Ax + {G}^{2} = 0$

we get

$\rm :\longmapsto\:2A = 10\rm \implies\:A = 5$

and

$\rm :\longmapsto\: {G}^{2} = 11 \:$

where,

A and G is the Arithmetic mean and Geometric mean between the roots of the quadratic equation.

Now, we know that,

If A, G and H are Arithmetic mean, Geometric mean and Harmonic mean of the series, then

$\rm :\longmapsto\:\boxed{ \tt{ \: \: {G}^{2} = A \times H \: \: }}$

So, on substitute the values of A and G, we get

$\rm :\longmapsto\:11 = 5 \times H$

$\red{\rm \implies\:\boxed{ \tt{ \: H \: = \: \frac{11}{5} \: \: }}}$

• Hence, Option (d) is correct