CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If b is the mean proportion between a and c, show that.
a4+a2b2+b4b4+b2c2+c4=a2c2

Open in App
Solution

We have
a4+a2b2+x4b4+b2c2+c4 =a2c2

We know that,
Mean proportion, b2=ac
a4+a2ac+(a2c2)2(a2c2)2+acc2+c4=a2c2

Taking L.H.S only
a4+a3c+a4c4c4+c3a+a4c4=a2c2
a3(a+c+ac4)c3(c+a+ca4)=a2c2
a2+ac+a2c4c2+ac+c2a4=1
a2+ac+a2c4=c2+ac+c2a4
a2c2=c2a4a2c4
(a2c2)=a2c2(a2c2)
a2c2=R.H.S

flag
Suggest Corrections
thumbs-up
4
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Proportions
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon