. find three numbers in ap whose sum is 9 and sum of their cubes is 153.
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let the terms be a-d, a, a+d
so, ATQ
a-d+a+a+d=9
3a=9
a=3
also,
(a-d)³+a³+(a+d)³=153
(3-d)³+3³+(3+d)³=153
3³-d³-3(3)²d+3(3)d²+3³+3³+d³+3(3)²d+3(3)d²=153
27+9d²+27+27+9d²=153
81+18d²=153
18d²=153-81
d²=72/18
d=√72/18
d=√4
d=±2
so,
the terms are 1, 3, and 5.
so, ATQ
a-d+a+a+d=9
3a=9
a=3
also,
(a-d)³+a³+(a+d)³=153
(3-d)³+3³+(3+d)³=153
3³-d³-3(3)²d+3(3)d²+3³+3³+d³+3(3)²d+3(3)d²=153
27+9d²+27+27+9d²=153
81+18d²=153
18d²=153-81
d²=72/18
d=√72/18
d=√4
d=±2
so,
the terms are 1, 3, and 5.
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