Question

find two consecutive positive even numbers whose square the sum is 130​

Answer 1

hello mate!!!

Solution:

let the two consecutive integers be x and x+2

their squares= x^2 and (x+2)^2

now,

x^2+(x+2)^2=130

x^2+x2+4x+4=130

2x^2+4x+4-130=0

2x^2+4x-126=0

now,

dividing both sides by 2

x^2+2x-63=0

x^2+9x-7x-63=0.....(splitting the middle term)

x(x+9)-7(x+9)=0

(x+9)(x-7)=0

Therefore,

x=-9 or x= 7

now,

let the first number be 7,

therefore, (7)^2=49

and consecutive number= x+2=7+2=9

therefore,

(9)^2=81

therefore,

49+81=130

also,

if x=-9 and x=-9+2=-7,

then, also 130 is the answer

hope this helps!! ☺✌❤