Question

Q2. The sum of LCM and HCF of two numbers is 8340. if the LCM of these numbers is 8300 more than their HCF ,then find the product of the two numbers is​

Answer 1

Question 1 :

$\sf{Given \:that \:\sin(\theta) = \dfrac{a}{b}, \: then \:\cos(\theta) \: is \:equal \:to}$

$:\implies\tt \sin^2(\theta) + \cos^2(\theta) = 1\\\\\\:\implies\tt\cos^2(\theta) = 1 - \sin^2(\theta)\\\\\\:\implies\tt\cos(\theta) = \sqrt{1 - \sin^2(\theta)}\\\\\\:\implies\tt\cos(\theta) = \sqrt{1 - \bigg(\dfrac{a}{b}\bigg)^{2} }\\\\\\:\implies\tt\cos(\theta) = \sqrt{1 - \frac{ {a}^{2} }{ {b}^{2} } }\\\\\\:\implies\tt\cos(\theta) = \sqrt{ \frac{ {b}^{2} - {a}^{2} }{ {b}^{2} } }\\\\\\:\implies \boxed{ \blue{\tt\cos(\theta) = \frac{ \sqrt{( {b}^{2} - {a}^{2}) }}{b}}}$

$\rule{200}{2}$

Question 2 :

The sum of LCM and HCF of two numbers is 8340. if the LCM of these numbers is 8300 more than their HCF, then find the product of the two numbers is.

$:\implies\tt HCF + LCM = 8340\\\\\qquad\scriptsize{\bf{\dag}\:\texttt{Given : LCM = 8300 + HCF}}\\\\:\implies\tt HCF + 8300 + HCF = 8340\\\\\\:\implies\tt 2HCF = 8340 - 8300\\\\\\:\implies\tt 2HCF = 40\\\\\\:\implies\tt HCF = \dfrac{40}{2}\\\\\\:\implies\tt HCF = 20$

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$\underline{\bigstar\:\textsf{Product of two Numbers :}}$

$\longrightarrow\tt Product\:of\:Numbers = HCF \times LCM\\\\\\\longrightarrow\tt Product\:of\:Numbers = HCF \times (8300+HCF)\\\\\\\longrightarrow\tt Product\:of\:Numbers = 20 \times (8300+20)\\\\\\\longrightarrow\tt Product\:of\:Numbers = 20\times8320\\\\\\\longrightarrow \boxed{\tt \blue{ Product\:of\:Numbers = 166400}}$

Answer 2

Step-by-step explanation:

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