# Thread: Two surds problems - one involving simultaneous equations..

1. ## Two surds problems - one involving simultaneous equations..

1. Two sides of a triangle are 5sqrt(3) and 10sqrt(2) respectively, while the hypotenuse is unknown. Here I tried finding the hypotenuse using pythagoras theorem.

x ^ 2 = (5sqrt(3))^2 + (10sqrt(2)) ^ 2

The answer on should be x = 5sqrt(11) but I get 5sqrt(3) + 10

2. Two simultaneous equations are as follows:

Code:
7x - (3sqrt(5))y = 9sqrt(5)           (1)
(2sqrt(5)x + y = 34                     (2)
I tried rearranging (1) to y = (9sqrt(5) - 7x) / 3sqrt(5) but I cannot reach an answer at all ..

P.S. Is there any tutorial on how to generate real maths symbols on this forum?

2. Hello, struck!

1. Two sides of a right triangle are $\displaystyle 5\sqrt{3}$ and $\displaystyle 10\sqrt{2}$
Find the hypotenuse.

$\displaystyle x^2 \:= \5\sqrt{3})^2 + (10\sqrt{2})^2$

$\displaystyle x^2 \;=\;5^2(\sqrt{3})^2 + 10^2(\sqrt{2})^2$

$\displaystyle x^2 \;=\;25(3) + 100(2) \;=\;75 + 200 \;=\;275$

$\displaystyle x \;=\;\sqrt{275} \;=\;\sqrt{25\!\cdot\!11} \;=\;\boxed{5\sqrt{11}}$

$\displaystyle 2)\;\;\begin{array}{cccc}7x - (3\sqrt{5})y &= &9\sqrt{5} & {\color{blue}[1]} \\ (2\sqrt{5})x + y &=& 34 & {\color{blue}[2]} \end{array}$

$\displaystyle \begin{array}{cccc}\text{Multiply {\color{blue}[2]} by }3\sqrt{5}\!: & 30x + 3\sqrt{5}\,y & = & 102\sqrt{5} \\ \text{Add {\color{blue}[1]}:} & 7x - 3\sqrt{5}\,y &=& 9\sqrt{5} \end{array}$

And we have: .$\displaystyle 37x \:=\:111\sqrt{5} \quad\Rightarrow\quad \boxed{x \:=\:3\sqrt{5}}$

Substitute into [2]: .$\displaystyle (2\sqrt{5})(3\sqrt{5}) + y \:=\:34 \quad\Rightarrow\quad 30 + y \:=\:34 \quad\Rightarrow\quad \boxed{y \:=\:4}$

3. P.S. Is there any tutorial on how to generate real maths symbols on this forum?
you can click on anyone's math symbols to see what they used to write something. Also, there is a branch of the forum where you can ask if you are having difficulty. This page might also come in handy