if the sum of the squares of three positive number is 14 and their sum of their product taking two at a time is 11 , find the sum of the number
Answers
Answered by
0
Answer:
6
Step-by-step explanation:
a power 2+b power 2+c power 2= 14
ab+bc+ac= 11
(a+b+c) square = a power 2+ b power 2+ c power 2+ 2(ab+bc+ac)
=14+2(11)
=36 = (a+b+c)= 6
Answered by
0
Answer:
Let the numbers be x and y. Then,
x+y=14
Let S be the sum of the squares of x and y. Then,
S=x
2
+y
2
S=x
2
+(14−x)
2
S=2x
2
−28x+196
dx
dS
=4x−28
dx
2
d
2
S
=4
The critical points of S are given by
dx
dS
=0.
4x−28=0⟹x=7
As,
dx
2
d
2
S
>0
Thus, S is minimum when x=7. Putting x=7, we get, y=7.
Hence, the required numbers are both equal to 7.
Similar questions