Sum of two consecutive square of number are 481. Find the sum of the two number

2 thoughts on “Sum of two consecutive square of number are 481. Find the sum of the two number”

1. let first number = X

   let second number = X+1

   square of the two number

   (X)^2 + (X+1)^2 =481

   x^2 + x^2+1+2x =481

   2x^2 +2x +1-481

   2(X2+x-240) =0

   X2 +X -240

   X2 +16x -15x -240

   X(X+16) -15(X+16)

   x-15) (X+16)

   X=15

   X=-16

   Reply

2. [tex]\large\bf{\underline{\underline{Question:−}}}[/tex]

   The sum of the squares of two consecutive positive integers is 481. Find the integers.

   [tex]\large\bf{\underline{\underline{Answer:−}}}[/tex]

   [tex]\color{red}\longrightarrow{}[/tex][tex]\rm{x² + (x+1)^2 = 481}[/tex]

   [tex]\color{red}\longrightarrow{}[/tex][tex]\rm{x^2 + x^2 + 2x + 1 = 481}[/tex]

   [tex]\color{red}\longrightarrow{}[/tex][tex]\rm{2x^2 + 2x + 1 – 481 = 0}[/tex]

   [tex]\color{red}\longrightarrow{}[/tex][tex]\rm{2x^2 + 2x – 480 = 0}[/tex]

   [tex]\underline\bold\color{purple}{Simplify,}[/tex]

   [tex]\sf{Divide\: by\: 2}[/tex]

   [tex]\rm{x^2 + x – 240 = 0}[/tex]

   [tex]\sf{Factors \:to}[/tex]

   [tex]\rm{(x+16)(x-15) = 0}[/tex]

   [tex]\sf{positive \:solution}[/tex]

   x=15 & 16 are the integers

   [tex]\tt{See \:if\: that\: works}[/tex]

   [tex]\color{teal}\underline{\underline{ \tt{{ \boxed {15^2 + 16^2 = 225 + 256 = 481} }}}}[/tex]

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   Thankyou 🙂

   Reply