Question

find the two consecutive numbers whose squares have the sum 85 {by quadratic equation formula) plzzz fast tomorrrow i need to submit

the sum of two numbers is 15 if their reciprocals is 3/10 find the two number using quadratic formula

Answer 1

Let the no. be =x
its consecutive no. be = x+1
According to question =
x^2 +(x+1)^2=85
x^2 + (x^2+1+2x) =85              {(a+b)^2=a^2+b^2+2ab}
2x^2+2x+1-85=0
2x^2+2x-84=0
x^2+x-42=0
x^2+7x-6x-42=0
x(x+7) -6(x+7)=0
(x+7) (x-6)=0
x=-7 , x=6

Answer 2

x²+ (X + 1 )²=85
(X )² + (x )²+ 2 X + 1 =85
2x²+2x-84