Question

Two numbers differ by 3. the sum of twice the smaller no. and thrice the greater no. is 19. find the numbers.
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Answer 1

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Answer 2

Question :-

Two numbers differ by 3. the sum of twice the smaller no. and thrice the greater no. is 19. find the numbers.

Answer :-

$\textbf{let \: x \: - y = 3}$

$\textbf{x \: = y + 3...(i)}$

Also , xy = 54

$\implies \textbf y ² (y + 3) = 54...(Using \:i)$

$\implies\textbf{y² + 3y - 5y = 0}$

$\implies \textbf{y² + 9y - 6y - 5y = 0}$

$\implies\textbf{y(y + 9) - 6(y + 9) = 0}$

$\implies\textbf{(y + 9)(y - 6)}$

$\implies\textbf{y( - 9) \: or \: y \: = 6}$

$\bf{puting \: y \: = - 9 \: in \: ..(i) } \: we \: get$

$\bf{x \: = - 9 + 3 = 6}$

$\bf{oc \: = \: 6 + 3 \: = 9}$

Hence , The Number are -6 and -9 , or 6

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