if a/b = b/c,prove that (a+b+c) (a-b+c)= a^2 + b^2 + c^2
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Answer:
To 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:
hope you help it
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