Math Question?

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solve for z: |9z-4| = |4z-3|

2007-02-20 17:57:06 · 2 answers · asked by chichidb18 2 in Science & Mathematics ➔ Mathematics

2 answers

you can either plot z = I9z-4I and z = I4z-3I to find the intersection points or solve the equation by squaring both sides. by squaring, you will eliminate negative values.

I9z-4I^2 = I4z-3I^2
81z^2 - 72z + 16 = 16z^2 - 24z + 9
65z^2 - 48z + 7 = 0

solve for z using:
z = [-b +/- sqr[b^2 - 4ac] ] / 2a

a=65, b=-48, c=7

= [-(-48) +/- sqr[(-48)^2 - 4(65)(7)]] / 2(65)
= 7/13 or 1/5

2007-02-20 18:50:33 · answer #1 · answered by sirius 2 · 0⤊ 0⤋

z solves that if and only if z solves at least one of

9z-4 = 4z-3 or 9z-4 = - (4z-3)

Surely you can take it from there.

2007-02-20 18:17:24 · answer #2 · answered by Curt Monash 7 · 0⤊ 0⤋