Question

if the sum of square of 2 numbers with sum 10 is 58.Find the numbers​

Answer 1

Step-by-step explanation:

Let 2x and 2x+2 be the required even numbers.

Given that the sum of squares numbers is 580.

Therefore,

(2x)

2

+(2x+2)

2

=580

4x

2

+4x

2

+4+8x=580

8x

2

+8x+4−580=0

8x

2

+8x−576=0

x

2

+x−72=0 (Taking 8 common)

x

2

+9x−8x−72=0

(x+9)(x−8)=0

x=−9 or x=8

Case I:- x=−9

Therefore, the required numbers are-

2x=2×−9=−18

2x++2=2×−9+2=−16

Case II:- x=8

Therefore, the required numbers are-

2x=2×8=16

2x+2=2×8+2=18

Hence the required numbers are −18 and −16 or 16 and 18.