if the sum of square of 2 numbers with sum 10 is 58.Find the numbers
Answers
Answer:
this is the correct answer
Step-by-step explanation:
The required A.P or numbers are 3,5,7 or 7,5,3.
Step-by-step explanation:
Given : The sum of 3 numbers in A.P is 15 and sum of squares of the extreme terms is 58.
To find : The numbers?
Solution :
Let The terms in A.P is a-d, a ,a+d.
According to question,
The sum of 3 numbers in A.P is 15.
i.e. a-d+a+a+d=15a−d+a+a+d=15
3a=153a=15
a=\frac{15}{3}a=
3
15
a=5a=5
The sum of squares of the extreme terms is 58.
(a-d)^2+(a+d)^2= 58(a−d)
2
+(a+d)
2
=58
a^2+d^2-2ad+a^2+d^2+2ad= 58a
2
+d
2
−2ad+a
2
+d
2
+2ad=58
2(a^2+d^2)= 582(a
2
+d
2
)=58
a^2+d^2= 29a
2
+d
2
=29
Substitute a=5,
5^2+d^2= 295
2
+d
2
=29
25+d^2= 2925+d
2
=29
d^2=29-25d
2
=29−25
d^2=4d
2
=4
d=\sqrt{4}d=
4
d=2,-2d=2,−2
Now, When a=5 and d=2 the AP is
a-d=5-2=3
a=5
a+d=5+2=7
The required A.P or numbers are 3,5,7.
Now, When a=5 and d=-2 the AP is
a-d=5+2=7
a=5
a+d=5-2=3
The required A.P or numbers are 7,5,3.