Question

find the constive no whose square have the sum of 85 ​

Answer 1

Solution:

let the consecutive numbers be x, x+1

now,

x^2+ (x+1)^2=85

x^2+x^2+ 2x+1=85

2x^2+2x-84=0

x^2+x-42=0........(required quadratic polynomial)[ dividing by 2]

by factorization method,

x^2+7x-6x-42=0

x(x+7)-6(x+7)=0

(x+7)(x-6)=0

x=-7 or x= 6

but natural numbers cannot be negative,hence x=-7 is discarded

therefore x= 6.

hence,

the number is = 6

and the next number= x+1= 6+1= 7

Checking

6 and 7 are consecutive numbers whose squares gave the sum 85

(6)^2+(7)^2=85

36+49= 85

85= 85

therefore

the numbers in the answer (6 and 7 ) are correct

similarly,

the numbers can be -6 and -7 too

as,

(-6) ^2+(-7) ^2= 85

36+49=85

85=85

hope this helps!!❤✌☺