if y=ax+b/cx+d prove that 2y1y3=3(y2)^2
if y=ax+b/cx+d prove that 2y1y3=3(y2)^2
taniska , 10 Years ago
Grade 12
Differential Calculus> if y=ax+b/cx+d prove that 2y1y3=3(y2)^2...
2 AnswersRinkoo Gupta
Last Activity: 10 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
Last Activity: 8 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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