Asked by su

Can anyone solve this without expanding:

(2x+9)**(1/5) = (9x-5)**(1/7)

Thanks in advance
Su
Answered by drwls
Does the ** represent multiplication (x) or raising to an exponent (^) ??

Your notation needs to be explained.

If you mean
(2x+9)/5 = (9x-5)/7, then
14x +63 = 45x -25
31x = 88
x = 88/31
Answered by su
No its an exponent not a fraction.
Answered by drwls
In that case
(2x+9)^(1/5) = (9x-5)^(1/7)
9x-5 = (2x+9)^(7/5)
9x = (2x+9)^(7/5) + 5
x = 0.2605
(I had to solve that by iteration)
Answered by su
If we put back the value .2605 in the equation and use the calculator we get on LHS (2*.2605 +9)^(1/5) = 1.5694
but on RHS( 9*.2605 -5)^(1/7) we get = -1.1497
so by iteration is also not correct ..
Answered by Reiny
I made up a "primitive" program in Quick-Basic and got a value of x = appr. -35.75

for that value
LS = (-62.5)^(1/5) = -2.286525
RS = ( -326.75)^(1/7) = -2.286513

not bad, eh?
Answered by su
I Still should be able to solve algebrically for a solution of -35.75 -This basically is a radical program.
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