My teacher said
If x-2(square root xy)=9-4(square root 2)
so since there are two square roots
-2(square root xy) equals -4(square root 2)
How is this possible, could the values be different and they are not equal.
your teacher is dead wrong.
example:
6-sqrt25=15-sqrt196
sqrt25 is not equal to sqrt196, ever.
Point this out to your teacher.
In the given equation, "x-2(square root xy) = 9-4(square root 2)", the equation is equated to another equation. It seems that your teacher is suggesting that the two terms involving square roots, "-2(square root xy)" and "-4(square root 2)", are equal to each other.
To determine if these two terms are indeed equal, we can set up the following equation:
-2(square root xy) = -4(square root 2)
To solve this equation, we can isolate the square root terms on one side:
-2(square root xy) + 4(square root 2) = 0
Next, let's factor out the common factor of "-2(square root xy)":
-2(square root xy)(1 - 2(square root 2/xy)) = 0
Now, for a product to be equal to zero, at least one of the factors must be zero. So we have two possibilities:
Case 1: The factor "-2(square root xy)" equals zero:
-2(square root xy) = 0
If we solve this equation for "xy", we get:
square root xy = 0
To find the value of "xy", we square both sides:
xy = 0^2
Thus, in this case, "xy" must be equal to zero.
Case 2: The factor "1 - 2(square root 2/xy)" equals zero:
1 - 2(square root 2/xy) = 0
If we solve this equation for "xy", we get:
1 = 2(square root 2/xy)
(square root 2/xy) = 1/2
Now, if we square both sides, we get:
2/xy = 1/4
Cross-multiplying gives:
8 = xy
Thus, in this case, "xy" must equal 8.
In conclusion, we have found two possible values for "xy": 0 and 8. This means that the terms "-2(square root xy)" and "-4(square root 2)" in the original equation can indeed be equal, with different values of "xy".