A number 15 is divided into three parts which are in
a.p. and the sum of their squares is 83. find the highest part.
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Since the parts are in A.P.
Let the Common difference is 'd' and middle part is 'a'.
(a-d)+a+(a+d) = 15
3a = 15
a = 5
Now, its given that
(a-d)² + a² + (a+d)² = 83
(a²+d²-2*a*d) + a² + (a²+d²+2*a*d) = 83
3*a² + 2*d² = 83
3*5² + 2*d² = 83
3*25 + 2*d² = 83
75 + 2*d² = 83
2*d² = 8
d² = 4
d = 2, -2
Using value of d, we get parts as
3,5,7
So the highest part is 7
Let the Common difference is 'd' and middle part is 'a'.
(a-d)+a+(a+d) = 15
3a = 15
a = 5
Now, its given that
(a-d)² + a² + (a+d)² = 83
(a²+d²-2*a*d) + a² + (a²+d²+2*a*d) = 83
3*a² + 2*d² = 83
3*5² + 2*d² = 83
3*25 + 2*d² = 83
75 + 2*d² = 83
2*d² = 8
d² = 4
d = 2, -2
Using value of d, we get parts as
3,5,7
So the highest part is 7
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