find the value of a and b when
Answers
Answer:
a=31/19, b= 10/19.
Explanation: 5+ root under 6/5-root under 6=
(5+ root under 6)²/19 [when we multiply it by 5+root under 6 ]
So,it is =31+10root under 6/19.
Hence, a=31/19, b= 10/19.
Question: Find the value of a and v when (5√6)/(5-√6) = a + b√6
Answer:
a = 31/19 and b = 10/19
Step-by-step explanation:
Given in the question that (5 + √6)/(5 - √6) = a + b√6. We need to find out the value of a and b.
Now,
Do rationalising of 5+√6/5-√6
[(5 + √6)(5 + √6)]/[(5 - √6)(5 + √6)] = a + b√6
Used identity: (a + b)(a - b) = a² - b²
(a + b)(a + b) = (a + b)²
(5 + √6)²/[(5)² - (√6)²] = a + b√6
(25 + 6 2(5)(√6)/(24 - 6) = a + b√6
(25 + 6 + 10√6)/(25-6) = a + b√6
(31 + 10√6)/19 = a + b√6
31/19 + 10√6/19 = a + b√6
On comparing a 31/19 + 10√6/19 with a + b√6 we get,
a = 31/19 and b = 10/19
Therefore, the value of a is 31/19 and b is 10/19.