Question 1156634
I read it this way:
{{{ x^2 + ( x + 2 )^2 = x + 2 + 67 }}}
{{{ x^2 + x^2 + 4x + 4 = x + 69 }}}
{{{ 2x^2 + 3x - 65 = 0 }}}
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Use quadratic formula:
{{{ x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = 2 }}}
{{{ b = 3 }}}
{{{ c = -65 }}}
{{{ x = (-3 +- sqrt( 3^2-4*2*(-65) ))/(2*2) }}}
{{{ x = (-3 +- sqrt( 9 + 520 )) / 4 }}}
{{{ x = (-3 +- sqrt( 529 )) / 4 }}}
{{{ x = ( -3 + 23 ) / 4 }}}
{{{ x = 20/4 }}}
{{{ x = 5 }}}
and
{{{ x = ( -3 - 23 ) / 4 }}} ( can't use the negative solution )
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The consecutive odd integers are: 5 and 7
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check:
{{{ x^2 + ( x + 2 )^2 = x + 2 + 67 }}}
{{{ 5^2 + ( 5 + 2 )^2 = 5 + 2 + 67 }}}
{{{ 25 + 49 = 74 }}}
{{{ 74 = 74 }}}
OK