the sum of 3 nos in AP is 18 and the sum of their square is 126 find nos
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Answered by
1
Answer:
Let the three numbers be (a−d),d,(a+d)
Sum of the three numbers=18
⇒a−d+a+a+d=18
⇒3a=18
⇒a=6
Sum of their squares=180
⇒(a−d)
2
+a
2
+(a+d)
2
=180
⇒(6−d)
2
+36+(6+d)
2
=180
⇒36+d
2
−12d+36+36+d
2
+12d=180
⇒2d
2
=180−108
⇒2d
2
=72
⇒d
2
=36
⇒d=6
∴a=6d=6
a−d=0
a=6
a+d=12
∴3 numbers in ascending order are 0,6,12.
Answered by
0
Answer:
Let the three numbers be (a−d),d,(a+d)
Sum of the three numbers=18
⇒a−d+a+a+d=18
⇒3a=18
⇒a=6
Sum of their squares=180
⇒(a−d)
2
+a
2
+(a+d)
2
=180
⇒(6−d)
2
+36+(6+d)
2
=180
⇒36+d
2
−12d+36+36+d
2
+12d=180
⇒2d
2
=180−108
⇒2d
2
=72
⇒d
2
=36
⇒d=6
∴a=6d=6
a−d=0
a=6
a+d=12
∴3 numbers in ascending order are 0,6,12.
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