Form a pair of simultaneous equations and solve them to find x and y, given they are rational numbers.
Questions 1: x-3+√(y+2) = -1 + √5
Question 2: 1 1/2 + √(x+2y) = 3x + y + 2/3√3
Any help is appreciated
Those are 2 separate questions.
Form a pair of simultaneous equations and solve them to find x and y, given they are rational numbers.
Questions 1: x-3+√(y+2) = -1 + √5
Question 2: 1 1/2 + √(x+2y) = 3x + y + 2/3√3
Any help is appreciated
Those are 2 separate questions.
What you have to do is:
1) Find either x as a function of y or y as a function of x. So manipulate one of the equations till you get x=... or y=...
2) Substitute x or y in the OTHER equation and solve for the remaining variable. Now you have the value of either x or y.
3) Fill in the value for your found x or y and you'll get your second value.
Good luck!
The first equation can be written as
$\displaystyle x=2+\sqrt{5}-\sqrt{y+2}.$
You're told that $\displaystyle x$ is rational, so there can't be a $\displaystyle \sqrt{5}$ on the RHS because this is irrational. It has to be removed, and the only way to do this is to put $\displaystyle y=3$, leading then to $\displaystyle x=2$.
The second equation can be solved using the same technique.