(1 + 3squareroot of 5)squared = p + qsquareroot of 5 where p and q are integers. What are the values of p and q?
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Originally Posted by Natasha1 (1 + 3squareroot of 5)squared = p + qsquareroot of 5 where p and q are integers. What are the values of p and q? $\displaystyle (1 + 3 \sqrt{5})^2 = p + q\sqrt{5}$. Expand the left hand side and match it with the bits you have on the right hand side.
Originally Posted by Natasha1 (1 + 3squareroot of 5)squared = p + qsquareroot of 5 where p and q are integers. What are the values of p and q? Calculate (1 + 3squareroot of 5)squared
what is 2 x 3squareroot of 5? Should it be treated like (a+b)squared? asquared + bsquared + 2ab
Last edited by mr fantastic; Oct 25th 2010 at 12:05 PM. Reason: Merged posts
Originally Posted by Natasha1 Should it be treated like (a+b)squared? Indeed.
right right... then lets see, is it 1 + 45 + 6squareroot of 10 = p + qsquareroot of 5
Originally Posted by Natasha1 right right... then lets see, is it 1 + 45 + 6squareroot of 10 = p + qsquareroot of 5 Yes. And 1 + 45 = 46. Now compare each side.
Originally Posted by Natasha1 right right... then lets see, is it 1 + 45 + 6squareroot of 10 = p + qsquareroot of 5 Hi Natasha1, It is $\displaystyle 46+6\sqrt{5}$ The 2 is multiplied by the coefficient of the radical, not what's inside. $\displaystyle 2ab=2(1)(3\sqrt{5})=6\sqrt{5}$
Last edited by masters; Oct 26th 2010 at 04:04 AM.
so p = 46 and q = 6 but the squareroots are both different? We have a 10 and a 5?
Oh so it's 46 + 6squareroot of 5 = p + qsquareroot of 5. Thanks a million gents!!
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