Answer:
(√3-√2)(√3+√2) = 1
1/√3-√2 = √3+√2
1/√3+√2 = √3-√2
Explanation:
To simplify the expression (√3-√2)(√3+√2), we can use the difference of squares formula, which states that (a-b)(a+b) = a^2 - b^2.
Applying this formula to our expression, we have:
(√3-√2)(√3+√2) = (√3)^2 - (√2)^2
Simplifying further:
= 3 - 2
= 1
So, the simplified expression (√3-√2)(√3+√2) equals 1.
Now, let's compute 1/√3-√2 and 1/√3+√2:
To compute 1/√3-√2, we need to rationalize the denominator. To do this, we multiply both the numerator and the denominator by the conjugate of the denominator, which in this case is √3+√2.
1/√3-√2 = (1/√3-√2) * (√3+√2)/(√3+√2)
Multiplying the numerators and the denominators:
= (√3+√2)/(√3-√2)(√3+√2)
= (√3+√2)/(3-2)
= (√3+√2)/1
= √3+√2
Therefore, 1/√3-√2 simplifies to √3+√2.
Similarly, to compute 1/√3+√2, we multiply both the numerator and the denominator by the conjugate of the denominator, which is √3-√2.
1/√3+√2 = (1/√3+√2) * (√3-√2)/(√3-√2)
Multiplying the numerators and the denominators:
= (√3-√2)/(√3+√2)(√3-√2)
= (√3-√2)/(3-2)
= (√3-√2)/1
= √3-√2
Therefore, 1/√3+√2 simplifies to √3-√2.
In summary:
(√3-√2)(√3+√2) = 1
1/√3-√2 = √3+√2
1/√3+√2 = √3-√2
I hope this explanation helps you understand the simplification and computation process. Let me know if you have any further questions!