Question 522022
Let
Ist Integer = x
2nd Integer = x+1

{{{(x+1)^2+(2x)^2=424}}}
{{{x^2+2x+1+(2x)^2=424}}}
{{{x^2+2x+1+4x^2=424}}}
{{{5x^2+2x+1=424}}}
{{{5x^2+2x+1-424=0}}}
{{{5x^2+2x-423=0}}}

Use

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


{{{a = 5}}}
{{{b = 2}}}
{{{c = -423}}}


{{{x = (-2 +- sqrt( 2^2-4*5*-423 ))/(2*5) }}}


{{{x = (-2 +- sqrt( 4+8460 ))/(10) }}}


{{{x = (-2 +- sqrt(8464))/(10) }}}


{{{x = (-2 +- 92)/(10) }}}


{{{x = (-2 - 92)/(10) }}} or {{{x = (-2 + 92)/(10) }}}


{{{x = (-94)/(10) }}} or {{{x = (90)/(10) }}}
 

{{{x=-9.4}}} or {{{x=9) }}}

{{{x=-9.4}}} inadmissible
{{{x=9) }}}


Ist Integer = x = 9
2nd Integer = x+1 = 9+1 = 10