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3 nos. in A.P. whose sum is 48

Such as the sum of their square is 800

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Let nos be x-d, x, x+d
then (x-d)+(x)+(x+d)=48
=> 3x+d -d =48
3x=48
x=48/3
x=16

now
(x-d)^2 + x^2 + (x+d)^2 = 800
x^2 + d^2 -2xd + x^2 +x^2 + d^2 + 2xd=800
3x^2 + 2d^2 =800
3*(16)^2 + 2d^2 =800
3*256 + 2d^2 =800
768 + 2d^2=800
2d^2=800-768= 32
d^2 = 32/2= 16
d=sqrt(16)
d=4

so numbers are x-d=16-4=12
x=16
x+4=16+4=20

Thanks

Zulfikar Ali

Posted on Jan 27, 2009

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