Question

let✓AM =1.89,HM=3.5, Calculate geometric mean​

Answer 1

Answer:

The relation between Arithmetic Mean, Geometric Mean and Harmonic Mean is given as:

$\boxed{ AM \times HM = GM^2}$

According to the question,

• Arithmetic Mean (AM) = 1.89
• Harmonic Mean (HM) = 3.5

Substituting the values in the above formula, we get:

→ 1.89 × 3.5 = GM²

→ 6.615 = GM²

→ GM = √ ( 6.615)

⇒ GM ≈ 2.57

Hence the value of the Geometric Mean (GM) is 2.57 approximately.

Formulas:

$1.\: \boxed{AM = \dfrac{a+b}{2}}\\\\\\2. \: \boxed{GM = \sqrt{ab}}\\\\\\3. \: \boxed{HM = \dfrac{2ab}{a+b}}$

Answer 2

${\large{\bold{\rm{\underline{Understanding \; the \; question}}}}}$

★ This question says that the value of AM is 1.89 and the value of HM is 3.5 given. We have to calculate the GM.

${\bf{Where,}}$

${\bull \sf \leadsto AM \: means \: Arithmetic \: means}$

${\bull \sf \leadsto HM \: means \: Harmonic \: means}$

${\bull \sf \leadsto GM \: means \: Geometric \: means}$

${\large{\bold{\rm{\underline{Given \; that}}}}}$

★ Arithmetic mean (AM) = 1.89

★ Harmonic mean (HM) = 3.5

${\large{\bold{\rm{\underline{To \; find}}}}}$

★ Geometric mean (GM)

${\large{\bold{\rm{\underline{Solution}}}}}$

★ Geometric mean (GM) = 2.57

${\large{\bold{\rm{\underline{Using \; concept}}}}}$

★ Formula to find Geometric mean (GM)

${\large{\bold{\rm{\underline{Using \; formula}}}}}$

★ Geometric mean (GM) = AM × HM = GM²

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

~ Let's use the given formula,

${\boxed{\boxed{\green{\sf{AM \times HM \: = GM^{2}}}}}}$

~ Let's put the values according to given formula..!

${\tt{:\implies AM \times HM \: = GM^{2}}}$

${\tt{:\implies 1.89 \times 3.5 \: = GM^{2}}}$

${\tt{:\implies 6.615 \: = GM^{2}}}$

${\tt{:\implies \sqrt{6.615} \: = GM}}$

${\tt{:\implies 2.57 \: = GM}}$

${\tt{:\implies GM \: = \: 2.57}}$

${\frak{Henceforth, \: 2.57 \: is \: the \: value \: of \: geometric \: mean}}$