Calculating -6 divided by a when a=1+√7
Understanding the given value of a
- Given that a=1+√7
- This means that a is equal to 1 plus the square root of 7
Calculating -6 divided by a
- We need to find the value of -6 divided by a
- Substituting the value of a into the expression, we get:
- -6 / (1+√7)
Rationalizing the denominator
- To simplify the expression, we need to rationalize the denominator
- Multiplying both the numerator and denominator by the conjugate of the denominator, which is (1-√7), we get:
- (-6*(1-√7)) / ((1+√7)*(1-√7))
Solving the expression
- Expanding the expression in the denominator, we get:
- (-6 + 6√7) / (1-7)
Final calculation
- Simplifying further, we get:
- (-6 + 6√7) / -6
- This simplifies to 1 - √7
Therefore, when a=1+√7, the value of -6 divided by a is 1 - √7.