Question

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.​

Answer 1

Step-by-step explanation:

$\huge{ \fcolorbox{purple}{pink}{ \fcolorbox{yellow}{green}{ \red{AnsWer}}}}$

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

${\sqrt{3} + \sqrt{5}) {}^{2}} = a/b$

$\large{ \blue{3 + 5 + 2 \sqrt{15 =a/b}}}$

$\large{ \green{8 + 2 \sqrt{15} = a/b}}$

$\large{ \orange{2 \sqrt{15} = (a/b) - 8}}$

$\large{ \red{2 \sqrt{15} = (a - 8b)/b}}$

$\large{ \pink{ \sqrt{15} = (a - 8b)/2b}}$

$\large{ \color{yellow}{a - (8b)/2b \: is \: a \: rational \: number}}$

Then $\sqrt{15}$ is also a rational number

But as we know $\sqrt{15}$ is an irrational number.

This is a contradication.

This contradication has arisen as our assumption is wrong.

${ \color{navy}{hence \: \sqrt{3} + \sqrt{5} {}^{2} \: is \: an \: irrational \: number}}$

$\large { \underline{ \underline{ \mathfrak{ \color{purple}{@HoneyStars♡}}}}}$