Solve (sqr 3)x + (sqr 2)x = 1

[tilly]

Sorry, not sure what topic this question is under! But I am having trouble with finding x in this equation and I am unsure of where to begin.

Solve (sqr 3)x + (sqr 2)x = 1

I've tried squaring both sides, but it didn't really seem to get me anywhere.

Any help is greatly appreciated!

 

[stapel]

Solve (sqr 3)x + (sqr 2)x = 1

As posted, your exercise is:

. . . . .\(\displaystyle \mbox{Solve: }\, \sqrt{\strut 3\,}\, x\, +\, \sqrt{\strut 2\,}\, x\, =\, 1\)

But this is just a linear equation which solves as:

. . . . .\(\displaystyle x\, =\, \dfrac{1}{\sqrt{\strut 3\,}\, +\, \sqrt{\strut 2\,}}\)

...with no squaring involved. Was this what you meant? It seems unlikely from what you describe:

I've tried squaring both sides, but it didn't really seem to get me anywhere.

Please reply showing what you've done, starting with a correct statement of the original equation; followed by the squaring of both sides; continuing on to the expansion, simplification, and isolation of the one remaining radical term; and then showing what happened when you squared both sides again.

Thank you!

 

[tilly]

Thak you!! Yes, that was what my question was. I realise now how it was just a matter of factorising the LHS. Sorry, next time if I have a question I will show my attempt. Thank you again for all your help!