Question

The sum of the squares of two positive integers is 208. If the squares of the
larger is 18 times the smaller number, find the numbers.
​

Answer 1

Answer:

I think your question is wrong pls check it ones

Answer 2

$\begin{gathered}\Large{\bf{\pink{\underline{LeT,}}}} \\ \end{gathered}$

• P & Q are two positive integers.

• P is greater than Q.

$\begin{gathered}\Large{\bf{\green{\underline{GiVeN,}}}} \\ \end{gathered}$

• The sum of the squares of two positive integers is 208.

$\begin{gathered}\longmapsto\:\:\bf\blue{P^2\:+\:Q^2\:=\:208}--(1) \\ \end{gathered} </p><p>$

$\begin{gathered}\bf\red{And,} \\ \end{gathered}$

• The square of the larger number is 18 times to the smaller number.

$\begin{gathered}\longmapsto\:\:\bf\orange{P^2\:=\:18Q\:}--(2) \\ \end{gathered}$

$\begin{gathered}\Large{\bf{\purple{\underline{To\:FiNd,}}}} \\ \end{gathered}$

• The numbers.

$\begin{gathered}\Large{\bf{\pink{\underline{CaLcUlAtIoN,}}}} \\ \end{gathered}$

↝ Putting the value of P² in equation (1), we get

$\begin{gathered}:\implies\:\:\bf{18Q\:+\:Q^2\:=\:208} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{Q^2\:+\:18Q\:-\:208\:=\:0} \\ \end{gathered} </p><p>$

$\begin{gathered}:\implies\:\:\bf{Q^2\:+\:26Q\:-\:8Q\:-\:208\:=\:0} \\ \end{gathered} </p><p>$

$\begin{gathered}:\implies\:\:\bf{Q\:(Q\:+\:26)\:-8\:(Q\:-\:26)\:=\:0} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{(Q\:+\:26)\:(Q\:-\:8)\:=\:0} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{Q\:+\:26\:=\:0\:~~~~or~~~~\:Q\:-\:8\:=\:0} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{Q\:=\:-\:26\:~~~~or~~~~\:Q\:=\:8} \\ \end{gathered}$

[NOTE ➛ It is given that both numbers are positive integers.]

$\begin{gathered}:\implies\:\:\bf\orange{Q\:=\:8} \\ \end{gathered} </p><p>$

$\begin{gathered}\bf\red{Now,} \\ \end{gathered}$

↝ Putting the value of Q in the equation (2), we get

$\begin{gathered}:\implies\:\:\bf{P^2\:=\:18\times{8}\:} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{P^2\:=\:144\:} \\ \end{gathered} </p><p>$

$\begin{gathered}:\implies\:\:\bf{P\:=\:\sqrt{144}\:} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{P\:=\:\pm\:12\:} \\ \end{gathered} </p><p>$

[NOTE ➛ It is given that number is a positive integer.]

$\begin{gathered}:\implies\:\:\bf\green{P\:=\:12\:} \\ \end{gathered} </p><p>$

$</p><p>\begin{gathered}\Large\bf\blue{Therefore,} \\ \end{gathered}$

The two positive integers are 12 & 8.