Instruction
1
The main method of solving such equations is a method of construction of both parts of the equation in the square. However. naturally, the first thing you need to get rid of the square root sign. Technically, this method is not complicated, but sometimes it can lead to trouble. For example, the equation v(2x-5)=v(4-7). Raising both sides to a square you will get 2x-5=4x-7. Is the equation to solve is not difficult; x=1. But the number 1 will not be a root of this equation. Why? The substitute unit in the equation instead of the value X. in the right And the left part will contain expressions that have no meaning, that is negative. This value is not valid for the square root. Therefore, 1 is a third root, and therefore this irrational equation has no roots.
2
So, irrational equation is solved using the method of squaring both parts. And after solving the equation, it is necessary to check, to cut off extraneous roots. This substitute was found in the roots of the original equation.
3
Consider one more example.
2+vх-3=0
Of course, this equation can be solved in the same way as the previous one. To transfer a composite equationthat does not have a square root on the right side and continue to use the method of squaring. obtained to solve rational equation and check the roots. But there is another way, more elegant. Enter a new variable; vх=y. Accordingly, you will get the equation 2y2+y-3=0. That is the usual quadratic equation. Find its roots; y1=1 and y2=-3/2. Then solve the two equations vх=1; vх=-3/2. The second equation has no roots from the first we find that x=1. Don't forget to test the roots.
2+vх-3=0
Of course, this equation can be solved in the same way as the previous one. To transfer a composite equationthat does not have a square root on the right side and continue to use the method of squaring. obtained to solve rational equation and check the roots. But there is another way, more elegant. Enter a new variable; vх=y. Accordingly, you will get the equation 2y2+y-3=0. That is the usual quadratic equation. Find its roots; y1=1 and y2=-3/2. Then solve the two equations vх=1; vх=-3/2. The second equation has no roots from the first we find that x=1. Don't forget to test the roots.
