Question

the arthamatic mean between two numbers is 34 and their geometry mean is 16 find numbers​

Answer 1

Given :-

• The arithmetic mean between two numbers is 34.

• Their geometry mean is 16.

To Find :-

• Numbers.

Solution :-

Let R and A be the numbers,

Case (I),

The arthamatic mean between two numbers is 34.

↪ R + A/2 = 34

↪ R + A = 68

↪ A = 68 - R ____________eqn.(1)

Case (II),

Their geometry mean is 16.

↪ √RA = 16

↪ RA = 16 × 16

↪ RA = 256 ___________eqn.(2)

Put eqn.(1) value in eqn. (2),

↪ R(68 - R) = 256

↪ R² - 68R + 256 = 0

↪ R(R - 64) - 4(R - 64) = 0

↪ (R - 64) (R - 4) = 0

↪ R = 64 , 4

Put R = 64 in eqn.(2),

↪ 64 × A = 256

↪ A = 256/64

↪ A = 4

Put R = 4 in eqn.(2),

↪ 4 × A = 256

↪ A = 256/4

↪ A = 64

↪ A = 4 , 64

Hence,

• The required number is 64 , 4 and 4 , 64.