Question 879320
<pre>
{{{(matrix(5,1,
The,year,somebody,was,born))}}}  {{{""=""}}}  {{{(matrix(9,1,
The,year,in,which,they,are,a,certain,age))}}}{{{""-""}}}{{{(matrix(2,1,That,age))}}}

Since he will be x in the year x², then

the year he was born is x²-x

Since that was in the twentieth century, we have the inequality:

{{{1900}}}{{{""<=""}}}{{{x^2-x}}}{{{""<=""}}}{{{1999}}}

{{{1900}}}{{{""<=""}}}{{{x^2-x}}}{{{""<=""}}}{{{1999}}}

{{{1900}}}{{{""<=""}}}{{{x^2-x}}} and {{{x^2-x}}}{{{""<=""}}}{{{1999}}}
 
Solve each inequality separately:

Solving the first inequality:

{{{1900}}}{{{""<=""}}}{{{x^2-x}}}

{{{"0"}}}{{{""<=""}}}{{{x^2-x-1900}}}

Get critical numbers by solving

{{{x^2-x-1900}}}{{{""=""}}}{{{"0"}}}

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

{{{x = (-(-1) +- sqrt( (-1)^2-4*(1)*(-1900) ))/(2*(1)) }}}

{{{x = (1 +- sqrt(1+7600 ))/2 }}}

{{{x = (1 +- sqrt(7601))/2 }}}

{{{x = (1 +- sqrt(7601))/2 }}}

{{{x = (1 +- 87.1837)/2}}}

We need consider only positive numbers
for somebody's age, so we'll use the + 
only.
{{{x = (1 + 87.1837)/2}}}
{{{x = (88.1837)/2}}}
{{{x = 44.092}}}

We use test value 44 

{{{"0"}}}{{{""<=""}}}{{{x^2-x-1900}}}
{{{"0"}}}{{{""<=""}}}{{{44^2-44-1900}}}
{{{"0"}}}{{{""<=""}}}{{{-8}}}
That's false
We test value 45 
{{{"0"}}}{{{""<=""}}}{{{x^2-x-1900}}}
{{{"0"}}}{{{""<=""}}}{{{45^2-45-1900}}}
{{{"0"}}}{{{""<=""}}}{{{80}}}

That's true so

{{{x>=44.092}}} and since x is an integer,

{{{x>=45}}}

-----------------

Solve the second inequality

{{{x^2-x}}}{{{""<=""}}}{{{1999}}}

{{{x^2-x-1999}}}{{{""<=""}}}{{{"0"}}}

Get critical numbers by solving

{{{x^2-x-1999}}}{{{""=""}}}{{{"0"}}}

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

{{{x = (-(-1) +- sqrt( (-1)^2-4*(1)*(-1999) ))/(2*(1)) }}}

{{{x = (1 +- sqrt(1+7996 ))/2 }}}

{{{x = (1 +- sqrt(7997))/2 }}}

{{{x = (1 +- sqrt(7997))/2 }}}

{{{x = (1 +- 89.4204)/2}}}

Again, we need consider only positive numbers
for somebody's age, so we'll use the + 
only.
{{{x = (1 + 89.4204)/2}}}
{{{x = (90.4204)/2}}}
{{{x = 45.2102}}

We use test value 45 

{{{x^2-x-1999}}}{{{""<=""}}}{{{"0"}}}

{{{45^2-45-1999}}}{{{""<=""}}}{{{"0"}}}

{{{-19}}}{{{""<=""}}}{{{"0"}}}

That is true.

We use test value 46 

{{{x^2-x-1999}}}{{{""<=""}}}{{{"0"}}}

{{{46^2-46-1999}}}{{{""<=""}}}{{{"0"}}}

{{{71}}}{{{""<=""}}}{{{"0"}}}

That is false.

So {{{x<=45.2102}}} and since x is an integer,

{{{x<=45}}}

So the inequality is 

{{{45<=x<=45}}}

Therefore x=45, and he will be 45 in the year 45² = 2025.

So he was born in the year x²-x or 45²-45 = = 2025-45 = 1980.

[At present he is 34 years old.  So if you know anybody who is 34
years old, you can tell them that they will be x in the year x² :)  ]

Edwin</pre>