Question

The sum of the squareof two consecutive positive even integer is 100 find the integer ​

Answer 1

Answer:

the sum of two consecutive even integers is 100

102=100

the consecutive numbers must be less than 10

what are the choices ?

8 and 6

6 and 4

4 and 2

82=64 and 62=36

64+36=100

6 and 8 are the integers

if you want negative integers also use -6 and -8 as well

Answer 2

ANSWER:-

Let the two consecutive positive integers be ,

x,(x+2)

According to the Question, sum of square is 100,

so,

x²+(x+2)²=100

=> x²+x²+4+4x=100

=> 2x²+4x+4=100

=>x²+2x+2=50

=> x²+2x-48=0

=> x²+8x-6x-48=0

=> x(x+8)-6(x+8)=0

=> (x-6)(x+8)=0

=> x=6 and x= -8 but due to positive we will take 8.

=>If x=6,

then it will be 6 and 8 and if 8 it will be 8 and 10.

but we cant take 8 and 10 as it will not satisfy so,we take 6 and 8 respectively.

These are two consecutive integers whose sum of square equals 100.

Ans.