Question 1118712
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Write 9/400 as the difference of two consecutive {{{integer}}} {{{highlight(cross(number))}}} <U>numbers</U> with {{{highlight(cross(exponent))}}} <U>exponents</U> {{{highlight(cross(as))}}} –2.
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<pre>
{{{1/x^2}}} - {{{1/(x+1)^2}}} = {{{9/400}}}


{{{((x+1)^2 -x^2)/((x^2*(x+1)^2))}}} = {{{9/400}}}


{{{(2x+1)/(x^2*(x+1)^2)}}} = {{{9/400}}}.


At this point, the solution can be find mentally and momentarily:  x = 4.


<U>Check</U>.   At x= 4,  {{{(2x+1)/(x^2*(x+1)^2)}}} = {{{(2*4+1)/(4*5)^2}}} = {{{9/20^2}}} = {{{9/400}}}.   ! Correct !
</pre>

By the way, &nbsp;x= -5 &nbsp;also works and is another solution :  &nbsp;&nbsp;{{{1/(-4)^2}}} - {{{1/(-5)^2)}}} = {{{9/400}}}.


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OK, &nbsp;I admit that you don't know English perfectly.


But do you know at least your native language ? ?