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if y=ax+b/cx+d prove that 2y1y3=3(y2)^2

if y=ax+b/cx+d  prove that 2y1y3=3(y2)^2

Grade:12

2 Answers

Rinkoo Gupta
askIITians Faculty 81 Points
9 years ago
y=ax+b/cx+d= a/c + (b-ad/c)/(cx+d)

y1=dy/dx= -(b-ad/c)/(cx+d)2

y2= 2(b-ad/c)/(cx+d)3

y3=-6(b-ad/c)/(cx+d)4

2y1y3=12.(b-ad/c)2/(cx+d)6

=3.(2(b-ad/c)/(cx+d)^3)2

=3.(y2 )^2

Thanks & Regards

Rinkoo Gupta
N
13 Points
7 years ago
y = (ax+b)/(cx+d) 
multipy and divide by c
y = (acx+bc)/c(cx+d)
add and subtract ad
y = (acx+ad+bc-ad)/c(cx+d)
take a common from the first two terms
y = a(cx+d) +bc-ad/c(cx+d)
y= [a(cx+d)/c(cx+d)] + [(bc-ad)/c(cx+d)]
cancelling (cx+d) from the first term
y = a/c + [(bc-ad)/c(cx+d)]
dividing the c
y = a/c + (b-ad/c)/(cx+d)
this is done so that the x remains in either the numerator or denominator which makes it easy to solve further

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