[tex]\huge\mathfrak\red{☟︎︎︎anwer✍︎}[/tex]
[tex]x ^{2} + (x + 2) {}^{2} = 650[/tex]
[tex]x {}^{2} + {x}^{2} + 4x + 4 - 650 = 0[/tex]
[tex]2x^{2} + 4x - 646 = 0[/tex]
[tex] {x}^{2} + 2x - 323 = 0[/tex]
[tex] {x}^{2} + 19x - 17x - 323 = 0[/tex]
[tex]x(x + 19) - 17(x + 19) = 0[/tex]
[tex](x + 19 = 0 \: or \: x - 17 = 0[/tex]
[tex]x = - 19 \: or \: x = 17[/tex]
[tex]since \: x > 0, \: x = - 19 \: is \: not \: possible[/tex]
[tex]x = 17 \: and \: x + 2 = 17 + 2 = 19[/tex]
[tex]\sf \colorbox{gold} {ANSWER BY ACHALMUCHHAL2}[/tex]
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Verified answer
[tex]\huge\mathfrak\red{☟︎︎︎anwer✍︎}[/tex]
Let the two consecutive odd integers be X and X+2, where X>0
the according to the given,
[tex]x ^{2} + (x + 2) {}^{2} = 650[/tex]
[tex]x {}^{2} + {x}^{2} + 4x + 4 - 650 = 0[/tex]
[tex]2x^{2} + 4x - 646 = 0[/tex]
[tex] {x}^{2} + 2x - 323 = 0[/tex]
[tex] {x}^{2} + 19x - 17x - 323 = 0[/tex]
[tex]x(x + 19) - 17(x + 19) = 0[/tex]
[tex](x + 19 = 0 \: or \: x - 17 = 0[/tex]
[tex]x = - 19 \: or \: x = 17[/tex]
[tex]since \: x > 0, \: x = - 19 \: is \: not \: possible[/tex]
[tex]x = 17 \: and \: x + 2 = 17 + 2 = 19[/tex]
thus, the required number are 17 and 19
[tex]\sf \colorbox{gold} {ANSWER BY ACHALMUCHHAL2}[/tex]