Rationalise the denominator of 1 + √3 ÷ (1 + √3)²
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Originally Posted by Detanon Rationalise the denominator and numerator of 1 + √3 ÷ (1 + √3)² Multiply the denominator by its conjugate.
Last edited by VonNemo19; Dec 17th 2009 at 06:04 AM.
How do you find the conjugate?
Originally Posted by Detanon How do you find the conjugate? Example: The conjugate of $\displaystyle a+b$ is $\displaystyle a-b$.
Originally Posted by Detanon Rationalise the denominator of 1 + √3 ÷ (1 + √3)² Hi Detanon, The conjugate of $\displaystyle a+b\sqrt{r}$ is $\displaystyle a-b\sqrt{r}$ $\displaystyle \frac{1+\sqrt{3}}{(1+\sqrt{3})^2}=\frac{1+\sqrt{3} }{4+2\sqrt{3}}$ Now, multiply numerator and denominator by $\displaystyle 4-2\sqrt{3}$
I got (1 + 2√3) ÷ 2. but in my book it says the answer is (5 + 3√3) ÷ 2
$\displaystyle \frac{1+\sqrt{3}}{(1+\sqrt{3})^2}=\frac{1+\sqrt{3} }{4+2\sqrt{3}} $ $\displaystyle \times \frac{4-2\sqrt{3}}{4-2\sqrt{3}}=\frac{4-2\sqrt{3}+4\sqrt{3}-6}{16-12}=\frac{-2+2\sqrt{3}}{4}=\frac{-1+\sqrt{3}}{2}$
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