Question

If the sum of two natural numbers is 8 and their product is 15, find the

numbers qudraticaly ​

Answer 1

Answer:

Let the first natural number be x. Sum of two natural numbers is 8 then other natural numbers will be 8 – x. According to question. Product of both natural numbers = 15 ⇒ x (8 – x) = 15 ⇒ 8x – x2 = 15 ⇒ x2 – 8x + 15 = 0 ⇒ x2 – (5 + 3)x + 15 = 0 ⇒ x2 – 5x – 3x + 15 = 0 ⇒ (x2 – 5x) – (3x – 15) = 0 ⇒ x (x – 5) – 3 (x – 5) = 0 ⇒ (x – 5) (x – 3) = 0 ⇒ x – 5 = 0 or x – 3 = 0 ⇒ x = 5 or x = 3 Thus, if First natural no. = 5 then Second natural no. = 8 if First natural no. = 3 or Second natural no. = 8Read more on Sarthaks.com - https://www.sarthaks.com/750796/if-the-sum-of-two-natural-numbers-is-8-and-the-product-is-15-then-find-numbers

Answer 2

$\begin{gathered}\begin{gathered}\bf Given - \begin{cases} &\sf{sum \: of \: two \: natural \: numbers \: is \: 8} \\ &\sf{product \: of \: these \: numbers \: is \: 15} \end{cases}\end{gathered}\end{gathered}$

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$\begin{gathered}\begin{gathered}\bf To \: Find :- \begin{cases} &\sf{two \: natural \: numbers} \end{cases}\end{gathered}\end{gathered}$

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$\begin{gathered}\begin{gathered}\bf Let \: - \begin{cases} &\sf{ ✬ \: first \: natural \: number \: be \: x} \\ &\sf{ ✬ \: second \: natural \: number \: be \: y} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\bf\red{According \: to \: statement}\end{gathered}$

$\sf\sf \:  ⟼ \:  x \: + \: y \: = \: 8$

$\sf \: \sf \:  ⟼ \: y \: = \: 8 \: - \: x \: - - - (1)$

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$\begin{gathered}\bf\red{According \: to \: statement}\end{gathered}$

$\sf \:  ⟼ \: product \: of \: two \: natural \: numbers \: is \: 15$

$\bf\implies \:x \: y \: = \: 15$

 ✬ On substituting the value of y from (1), we get

$\sf \: \sf \:  ⟼ x \: ( \: 8 \: - \: x \: ) \: = \: 15$

$\sf \:  ⟼ \: 8 \: x \: - \: {x}^{2} \: = \: 15$

$\bf\implies \: {x}^{2} \: - \: 8 \: x \: + \: 15 \: = \: 0$

$\sf \:  ⟼ \: {x}^{2} \: - \: 5x\: - \: 3x \: + 15 \: = \: 0$

$\sf \:  ⟼ \: x \: ( \: x \: - \: 5 \: ) \: - 3 \: ( \: x\: - \: 5 \: ) \: = \: 0$

$\sf \:  ⟼ \: ( \: x \: - \: 5\: ) \: ( \: x \: - \: 3\: ) \: = \: 0$

$\bf\implies \:x \: = \: 5\: or \:x \: = \: 3$

$\sf \:  ⟼ \: So, \: when \: \bf \:  x \: = \: 3 \: \bf\implies \: y \: = \: 5$

$\sf \:  ⟼ \: And, \: when \: \bf \:  x \: = \: 5 \: \bf\implies \: y \: = \: 3$

$\bf \:  Hence, \: two \: natural \: numbers \: are \: 3 \: and \: 5.</p><p>$