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# Find all values of x satisfying (sqrt4x-3) + (10/sqrt4x-3) =7

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Find all values of x satisfying (sqrt4x-3) + (10/sqrt4x-3) =7

waffles  Oct 22, 2017
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√[ 4x - 3 ]  + 10 / √[ 4x - 3]  = 7

Let √ [ 4x - 3]  = a

So we have

a + 10/a  = 7           multiply through by a

a^2 + 10  = 7a      subtract 7a from both sides

a^2 - 7a + 10  = 0     factor

( a - 5) (a - 2)  = 0

Setting each factor to 0 and solving produces a = 5  or a  = 2

So.....

√ [ 4x - 3]  =  5      square both sides

4x - 3  = 25           add 3 to both sides

4x  = 28                divide both sides by 2

x  = 7

or

√ [ 4x - 3] = 2   square bot sides

4x - 3  =   4      add 3 to both sides

4x  = 7           divide both sides by 4

x =  7/4

CPhill  Oct 22, 2017

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