if a÷b = b÷c then prove (a^2 +b^2+c^2)÷(a-b+c)=a+b+c
Answers
Answered by
1
Answer:
Prove : (a+b+c)(a−b+c)=a
2
+b
2
+c
2
Proof : a,b,c are in continued proportion.
∴
b
a
=
c
b
=k (let)
b=ck
a=bk=(ck)k =ck
2
L.H.S. =(ck
2
+ck+c)(ck
2
−ck+c)
=c
2
(k
2
+k+1)(k
2
−k+1)
=c
2
[(k
2
+1)
2
−(k)
2
]
=c
2
[k
4
+2k
2
+1−k
2
]
=c
2
[k
4
+k
2
+1]
R.H.S. =c
2
k
4
+c
2
k
2
+c
2
=c
2
[k
4
+k
2
+1]
L.H.S = R.H.S.
Step-by-step explanation:
mark me as brainlist
Similar questions