A father is now 3 times as old as his son. 5 years ago he was 4 times as old as his son. Find their
present ages.​

1 thought on “A father is now 3 times as old as his son. 5 years ago he was 4 times as old as his son. Find their<br />present ages.​”

1. Step-by-step explanation:

   [tex] \huge{ \fcolorbox{purple}{pink}{ \fcolorbox{yellow}{green}{ \red{AnsWer}}}}[/tex]

   Let us assume to the contrary that [tex]( \sqrt{3} + \sqrt{5}) {}^{2} [/tex] is a rational number, then there exists a and b co- prime integers such that,

   [tex]{\sqrt{3} + \sqrt{5}) {}^{2}} = a/b[/tex]

   [tex] \large{ \blue{3 + 5 + 2 \sqrt{15 =a/b}}}[/tex]

   [tex] \large{ \green{8 + 2 \sqrt{15} = a/b}}[/tex]

   [tex] \large{ \orange{2 \sqrt{15} = (a/b) – 8}}[/tex]

   [tex] \large{ \red{2 \sqrt{15} = (a – 8b)/b}}[/tex]

   [tex] \large{ \pink{ \sqrt{15} = (a – 8b)/2b}}[/tex]

   [tex] \large{ \color{yellow}{a – (8b)/2b \: is \: a \: rational \: number}}[/tex]

   Then [tex] \sqrt{15} [/tex] is also a rational number

   But as we know [tex] \sqrt{15} [/tex] is an irrational number.

   This is a contradication.

   This contradication has arisen as our assumption is wrong.

   [tex] { \color{navy}{hence \: \sqrt{3} + \sqrt{5} {}^{2} \: is \: an \: irrational \: number}}[/tex]

   [tex] \large { \underline{ \underline{ \mathfrak{ \color{purple}{@HoneyStars♡}}}}}[/tex]

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