Question

The sum of squares of 4 consecutive natural number is 5334.The smallest of these numbers is

Answer 1

Answer

x²+(x+1)²+(x+2)²+(x+3)²=5334

x²+x²+1+2x+x²+4+4x+x²+9+6x=5334

4x²+12x+14=5334

4x²+12x=5320

x²+3x=1330

x²+3x-1330=0

x²+38x-35x-1330=0

x(x+38)-35(x+38)=0

(x+38)(x-35)=0

so x=-38 or x=35.

so Smallest no.=35