Author Topic: WTH Different calculator answers (Read 580 times) Tweet Share

kenhung123 · « **on:** April 17, 2010, 11:23:06 pm »

This is what I did:
$\sqrt{9x}=\frac{9x}{4}+1<br />\rightarrow <br />\frac{81x^{2}}{16}-9x+1=0<br />\rightarrow$
x=0.119 or x=1.66

But if I solve directly for x
$\sqrt{9x}=\frac{9x}{4}+1<br />$ THis gives x=4/9

brightsky · « **Reply #1 on:** April 17, 2010, 11:25:23 pm »

The squaring.

$(\sqrt{9x})^2 = \left(\frac{9x}{4} + 1 \right)^2$

$\implies 9x = \frac{81x^2}{16} + \frac{18x}{4} + 1$

Hence...

$\implies \frac{81x^2}{16} + \frac{18x}{4} - 9x + 1 = 0$

$\implies \frac{81x^2}{16} - \frac{18x}{4} + 1 = 0$

$\implies \frac{81}{16}x^2 - \frac{9}{2}x + 1 = 0$

Factorising LHS gives:

$\implies \frac{1}{16} (9x - 4)^2 = 0$

...which yields your answer of $x = \frac{4}{9}$

kenhung123 · « **Reply #2 on:** April 17, 2010, 11:29:26 pm »

ahhhh thanks!

Ilovemathsmeth · « **Reply #3 on:** April 18, 2010, 12:27:05 am »

Common mistake, don't forget to always expand brackets.

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Author Topic: WTH Different calculator answers (Read 580 times) Tweet Share

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WTH Different calculator answers

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