If a² + 2b = 7,b² +4c =-7 , c²+6a=-14
then value of( a²+b² +c²) is
Answers
Answered by
2
Step-by-step explanation:
Consider the given equations a
2
+2b=7, b
2
+4c=−7 and c
2
+6a=−14 and add them as follows:
a
2
+2b+b
2
+4c+c
2
+6a=7−7−14
⇒a
2
+b
2
+c
2
+6a+2b+4c=−14
⇒a
2
+b
2
+c
2
+6a+2b+4c+14=0
⇒(a
2
+6a+9)+(b
2
+2b+1)+(c
2
+4c+4)=0
⇒(a+3)
2
+(b+1)
2
+(c+2)
2
=0(∵(a+b)
2
=a
2
+b
2
+2ab)
⇒(a+3)
2
=0,(b+1)
2
=0,(c+2)
2
=0
⇒a+3=0,b+1=0,c+2=0
⇒a=−3,b=−1,c=−2
⇒a
2
=(−3)
2
,b
2
=(−1)
2
,c
2
=(−2)
2
⇒a
2
=9,b
2
=1,c
2
=4
Therefore, a
2
+b
2
+c
2
=9+1+4=14
Hence, a
2
+b
2
+c
2
=14.
I HOPE THIS HELPS U
Answered by
1
Answer:
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