SOLUTION: Please could you help with this equation Solve the following equation for x ( 3coshx + 5sinhx = 8) I've this far but can't finish the rest 3coshx + 5sinhx = 8 3[ex+/-x]

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Question 26641: Please could you help with this equation
Solve the following equation for x ( 3coshx + 5sinhx = 8)
I've this far but can't finish the rest
3coshx + 5sinhx = 8
3[ex+/-x]/2+5[ex-e-n] = 8
1.5 [ex+-x]+2.5[ex-e-x] = 8
1.5ex+1.5ex+2.5ex-2.5e-x = 8
4ex-1x = 8
4(ex)2 � 8ex-1 = 0
A B C

Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website!
3coshx + 5sinhx = 8
FOR SIMPLICITY LET US DENOTE ....E^X=A...SO ...E^(-X)=1/A...HENCE
COSH X = (A+1/A)/2...AND .....SINH X=(A-1/A)/2...SO WE HAVE
3(A+1/A)/2+5(A-1/A)/2=8...MULTIPLYING BY 2
3A+3/A+5A-5/A=16
8A-2/A=16.....DIVIDING BY 2 WE GET
4A-1/A-8=0....OR MULTIPLYING BY A...
4A^2-8A-1=0
USING QUADRATIC FORMULA..
WE GET ..
..
..
..=E^X...WHERE FROM YOU CAN GET X USING LOGS
X=LN{1+0.5(0.5)^(0.5)}