If a,b,c,d,e,f,g,h are 8 consecutive natural nos. then prove that a^2+d^2+f^2+g^2=b^2+c^2+e^2+h^2.?

Question

atleast try to answer!

Answer 1

b=a+1
c=a+2
d=a+3
e=a+4
f=a+5
g=a+6
h=a+7
a^2+d^2+f^2+g^2
=a^2+(a+3)^2+(a+5)^2+(a+6)^2
=4a^2+28a+70
b^2+c^2+e^2+h^2
=(a+1)^2+(a+2)^2+(a+4)^2+(a+7)^2
=4a^2+28a+70
hence proved

Answer 2

The left side is:

a^2 + (a+3)^2 + (a+5)^2 + (a+6)^2

= 4a^2 + 2(3+5+6)a + (3^2+5^2+6^2)

The right side is:

(a+1)^2 + (a+2)^2 +(a+4)^2 + (a+7)^2

= 4a^2 + 2(1+2+4+7)a + (1^2+2^2+4^2+7^2)

But

1+2+4+7 = 14 = 3+5+6

and

1^2+2^2+4^2+7^2 = 70 = 3^2 + 5^2 + 6^2

So the left side and right side are equal.