What can be the quadratic equation for the situation:
Sum of squares of two consecutive numbers is 145.

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Solution

Let first number is $x$

Second number will be $x + 1$

According to the statement

 ${(x)}^{2}$ + ${(x + 1)}^{2} = 145$

${(x)}^{2} + {(x)}^{2} + {(1)}^{2} + 2 x = 145$
[using the identity [ ${(a + b)}^{2}$ = ${(a)}^{2}$ + ${(b)}^{2} + 2 a b$ ]

$2 x^{2} + 2 x + 1 - 145 = 0$
$2 x^{2} + 2 x - 144 = 0$

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What can be the quadratic equation for the situation: Sum of squares of two consecutive numbers is 145.

Let first number is x Second number will be x+1 According to the statement  (x)2 + (x+1)2=145 (x)2+(x)2+(1)2+2x=145 [using the identity [ (a+b)2 = (a)2 + (b)2+2ab ] 2x2+2x+1−145=0 2x2+2x−144=0

What can be the quadratic equation for the situation:
Sum of squares of two consecutive numbers is 145.