find three numbers in AP whose sum is 15 and product is 80
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LET the numbers be (a-d), a and (a+d)
Then,
(a-d) + a + (a+d) = 15
3a = 15
a = 5
And,
(a-d)a(a+d) = 80
a(a²-d²)= 80
5(5²-d²) = 80
5(25-d²) = 80
-5d² = 80-125
-5d² = -45
d² = 45/5
d² = 9
d =✓9 = 3
THEREFORE,
first number = a-d = 5-3 =2
second number = 5
Third number = a+d = 5+3 = 8
Then,
(a-d) + a + (a+d) = 15
3a = 15
a = 5
And,
(a-d)a(a+d) = 80
a(a²-d²)= 80
5(5²-d²) = 80
5(25-d²) = 80
-5d² = 80-125
-5d² = -45
d² = 45/5
d² = 9
d =✓9 = 3
THEREFORE,
first number = a-d = 5-3 =2
second number = 5
Third number = a+d = 5+3 = 8
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