I a, b, c are in continued
continued proportion
show that
proportion
(a+b) ² - (b+c)
ab be
ab
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Answer:
To Prove : (a+b+c)(a−b+c)=a2 +b2 +c2
Proof : a,b,c are in continued proportion.
a/b=c/d =k (let)
b=ck
a=bk=(ck)k =ck2
L.H.S. =(ck2 +ck+c)(ck2 −ck+c)
=c2 (k2 +k+1)(k2 −k+1)
=c2 [(k2 +1) 2 −(k) 2 ]
=c2 [k4 +2k2 +1−k2 ]
=c2 [k4 +k2 +1]
R.H.S. =c2 k4 +c2 k2 +c2
=c2 [k4 +k2 +1]
L.H.S = R.H.S.
Step-by-step explanation:
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