The sum of squares of two consecutive numbers is 313.Hence find the required quadratic equation.

Explanation

Let x be any number.
`:.` The next or the provieous number of x is (x+1) and (x-1) respectivly.
As per question, `(x-1)^(2)+x^(2)=313andx^(2)+(x+1)^(2)=313.`
or, `x^(2)-2x+1+x^(2)=313 or, x^(2)+x^(2)+2x+1=313.`
or, `2x^(2)-2x-312=0or,2x^(2)+2x-312=0`
or, `x^(2)-x-156=0or,x^(2)+x-156=0`
Hence, the required quadratic equations in one variable are `x^(2)-x-156=0or,x^(2)+x-156=0`