Express 3 - 5 uderroot 5 upon 3 + 2 under root 5 in the form bracket a under root 5 minus b where A and B are simple fractions
Answers
Answer:
Step-by-step explanation:
Given Express 3 - 5 under root 5 upon 3 + 2 under root 5 in the form bracket a under root 5 minus b where A and B are simple fractions
Assuming the question to be
3 - 5√5 /3 + 2√5
Rationalizing the denominator we get
3 - 5√5 / 3 + 2√5 x 3 - 2√5 / 3 - 2√5
(3 - 5√5)^2 / 9 - 20
9 - 30√5 + 125 / - 11
134 - 30√5 / - 11
According to question A and B are fractions so we can keep as
30 √5/11 - 134 / 11
Answer:
Step-by-step explanation:
Given mathematical expression is : (3 - 5√5)/(3 +2√5)
Desired result: (a√5 - b) where a and b are simple fractions
We can try rationalizing the denominator of above expression and see if we arrive at the result.
On Rationalization:
(3 - 5√5)/(3 + 2√5) = (3 - 5√5) x (3 - 2√5) /(3 + 2√5) x (3 - 2√5)
= ( 9 - 6√5 - 15√5 + 50)/ (9 - 20)
= (59 - 21√5) / (-11)
On rearranging the final expression:
(21/11)√5 - 59/11
Comparing to the required outcome a√5 - b
we get a = 21/11
b = 59/11